I notice many references in the Qur'an, to "wealth and sons", in particular, God warning the pagans that their wealth and sons will not avail them in the end.
What pagan belief about wealth and sons was God addressing with these warnings?
These verses in first place show the importance of good deeds
In the Qur'an you may find that Allah mentions wealth (money and property) and children (sons) together in a couple of verses like in:
And know that your properties and your children are but a trial and that Allah has with Him a great reward. (8:28)
So let not their wealth or their children impress you. Allah only intends to punish them through them in worldly life and that their souls should depart [at death] while they are disbelievers. (9:55)
Wealth and children are [but] adornment of the worldly life. But the enduring good deeds are better to your Lord for reward and better for [one's] hope. (18:46)
Ibn Kathir commented on this saying:
(Wealth and children are the adornment of the life of this world.)
This is like the Ayah:
(Beautified for men is the love of things they covet; women, children, vaulted hoards of gold...) (3:14).
(Your wealth and your children are only a trial, whereas Allah! With Him is a great reward (Paradise).) (64:15) turning towards Allah and worshipping Him is better for you than keeping busy with them, and accumulating wealth for them and going to extremes in feeling pity and compassion for them.
Allah says: (But the good righteous deeds that last, are better with your Lord for reward and better for hope.)
Ibn 'Abbas, Sa'id bin Jubayr and others among the Salaf said that the good righteous deeds that last are the five daily prayers.
'Ata' bin Abi Rabah and Sa'id bin Jubayr narrated from Ibn 'Abbas,
"The good righteous deeds that last are "Subhan Allah (glory be to Allah)", "Al-Hamdu Lillah (praise be to Allah)", "La ilaha illallah (there is none worthy of worship except Allah)", and "Allahu Akbar (Allah is Most Great)."
The Commander of the faithful, 'Uthman bin 'Affan was questioned, "Which are the good righteous deeds that last" He replied, "They are: "La ilaha illallah, Subhan Allah, Al-Hamdu Lillah, Allahu Akbar and La hawla wa la quwwata illa billah hil-'Aliyil-'Azim (there is no strength and no power except with Allah the Exalted, the Almighty)."
This was recorded by Imam Ahmad. Imam Ahmad also recorded from a freed slave of the Messenger of Allah that he said:
(Well done! Well done for five things! (How heavy they will weigh in the balance! "La ilaha illallah, Allahu Akbar, Subhan Allah, and Al-Hamdu Lillah," and a righteous son who dies and his parents seek the reward of Allah.) And he said: (Well done! Well done for five things! Whoever meets Allah believing in them, he will enter Paradise; if he believes in Allah, the Last Day, Paradise and Hell, resurrection after death, and the Reckoning). (Source qtafsir)
These final narrations and statements make clear that remembrance of Allah have a higher value by Allah.
The Day when there will not benefit [anyone] wealth or children (26:88)
Ibn Kathir commented on this saying:
(The Day whereon neither wealth nor sons will avail,)
means, a man's wealth will not protect him from the punishment of Allah, even if he were to pay a ransom equivalent to an earthful of gold.
means, "or if you were to pay a ransom of all the people on earth." On that Day nothing will be of any avail except faith in Allah and sincere devotion to Him, and renunciation of Shirk and its people. (Source qtafsir)
So this verse is again one of those who make clear that wealth and children are worldly matters which don't count without having performed good deeds in the hereafter.
And it is not your wealth or your children that bring you nearer to Us in position, but it is [by being] one who has believed and done righteousness. For them there will be the double reward for what they did, and they will be in the upper chambers [of Paradise], safe [and secure]. (34:37)
Ibn Kathir commented on this saying:
(And it is not your wealth, nor your children that bring you nearer to Us,) meaning, "these things are not a sign that We love you or care for you." (Source qtafsir)
And quoted this sahih hadith to show that good deeds and clean hearts are what would be of use in the day of judgement.
Know that the life of this world is but amusement and diversion and adornment and boasting to one another and competition in increase of wealth and children - like the example of a rain whose [resulting] plant growth pleases the tillers; then it dries and you see it turned yellow; then it becomes [scattered] debris. And in the Hereafter is severe punishment and forgiveness from Allah and approval. And what is the worldly life except the enjoyment of delusion. (57:20)
This verse is very expressive and shows the value of this worldly life and give an example for us to warn us and to remember Allah!
O you who have believed, let not your wealth and your children divert you from remembrance of Allah . And whoever does that - then those are the losers. (63:9)
Your wealth and your children are but a trial, and Allah has with Him a great reward. (64:15)
Don't this verses apply to us and every generation of humans too?
Note that on cannot conclude from these verses a clear relation to (former) pagan belief. But it is rather usual and still a "custom" that people gather money and wealth to leave it for their children. Therefore quoting both makes sense as there's a clear traceable relation between both.
In the sunnah we find in Sunan ibn Majah, Musnad Ahmad, at-Tabarni's al-Kabir (similar to the wording of al-Mustadrak), al-Bayhaqi in his sunan al-Kubra (narrated via his teacher al-Hakim = same wording as al-Mustadrak) etc. the following hadith:
"Hasan and Hussain came running to the Prophet (ﷺ) and he embraced them and said: 'Children make a man a miser and a coward.'" (Wording of Sunan ibn Majah and the Musnad)
Al-Hakim narrated in his al-Mustadrak a similar narration on the condition of Muslim -as confirmed by imam a-Dhahabi- saying (My own translation):
إن الولد مبخلة مجبنة مجهلة محزنة
Children make a man a miser, a cowar, a fool and a mourner
Imam al-'Iraqi after confirming the sanity of the sanad commented this briefly one could conclude from his statement the following explantion:
Therefore Allah told us that our wealth and children -which are both gifts from Allah- are a trial for us. As they might lead some of us to loose the balance we are asked to keep see for example:
And thus we have made you a just community that you will be witnesses over the people and the Messenger will be a witness over you. ... (2:143)
And [they are] those who, when they spend, do so not excessively or sparingly but are ever, between that, [justly] moderate (25:67)
Note that also our care or an excessive care for our children or gaining wealth might lead us to go astray as we may not pray on time, not do charity, not gain knowledge nor be a positive part or helping hand for the Muslim community in whatever need it might be. So they might divert us from remembering Allah, from worshiping Allah and following His orders -which is the main reason for our existence according Islam-. We also concentrate on the worldly matters and forget the hereafter while this life is action and no reckoning, but in the hereafter there will be the reckoning and no action.
Therefore it makes clearly sense to quote both wealth and offspring in one sentence or one verse as there's a clear connection between both as shown and this doesn't necessarily mean that this is connected to any pagan belief, it is rather a related to human nature which can -in cases- go astray or be to excessive in some of its concerns and deeds.
Some aspects of the pre-Islamic society
Finally note that the pre Islamic Arabs considered being wealthy, having (many) children, offspring and relatives -which are strong signs of tribalism and signs of their concentration on worldly matters- as a sign of honour, but Allah told us:
Whoever desires honor [through power] - then to Allah belongs all honor. To Him ascends good speech, and righteous work raises it. But they who plot evil deeds will have a severe punishment, and the plotting of those - it will perish. (35:10)
So if you look for a pagan belief one may conclude that it is rather their disbelief in the hereafter which is addressed as they -or some of them- seem to believe only in this life as stated in the Qur'an:
Life is not but our worldly life - we die and live, but we will not be resurrected. (23:37)
And they say, "There is not but our worldly life; we die and live, and nothing destroys us except time." And they have of that no knowledge; they are only assuming. (45:24)