The hadith you are referring to is:
'A’isha (RAA) narrated, ‘I asked the Messenger of Allah (ﷺ) ‘O Messenger of Allah (ﷺ), if I know what night the night of Qadr is, what should I say during it?’ He said, “Say:
O Allah, You are the Pardoner and You love to pardon, so pardon me."
Related by the five Imams except for Abu Dawud. At-Tirmidhi and Al-Hakim reported it as Sahih. (Bulugh al-Maraam)
The exact night corresponding to laylatul qadr is basically unknown (like it is the case for the certain hour on the day of Jumu'a, see in Timing of a certain hour on Friday). Maybe the reason and goal for this ambiguity is simply to make us do more efforts in certain time in the hope that Allah may accept our deeds.
The only clear and certain hint we have is that it is among the last ten nights of Ramadan this is the only mutuality between all reports.
Note that the list below may cover a whole bunch of reports, but there are certainly some missing ones that may even differ from the other ones covered here.
- Many reports say it is in the last ten nights of Ramadan like on the authority of 'Aisha in Sahih al-Bukhari (also in Jami' at-Tirmidhi and Sahih Muslim), on the authority of abu Hurrairah in Sahih Muslim and on the authority of ibn 'Omar in Sahih Muslim here and here(where some narrator was in doubt whether he said ten or nine).
- Some say in the last seven nights like on the authority of ibn 'Omar in Muwatt'a Malik (and Sunan abi Dawod) and in Sahih al-Bukhari and in Sahih Muslim (for those who were not able to do efforts from the ten last days on).
- Some say in the odd nights among the last ten nights (referring to 21st, 23rd, 25th, 27th and 29th) this was narrated on the authority of 'Aishah in Sahih al-Bukhari and abu Sa'id al-Khudry in Sahih al-Bukhari and Sahih Muslim.
- Some say it is among the 21st, 23rd and 25th night which was narrated on the authority of ibn 'Abbas in Sahih al-Bukhari, abu Sa'id al-Khudri in Sahih Muslim and 'Ubadah ibn as-Samit in Sahih al-Bukhari.
- Some reported that it is on the 23rd night of Ramadan like the narration on the authority of 'Abdullah ibn Unais in Sahih Muslim.
- Some others reported that it is on the 27th night of Ramadan like in the narration on the authority of Ubay ibn Ka'ab in Sahih Muslim and on the authority of abu Hurairah in Sahih Muslim (which is based on a conclusion of the given description).
So basically to be on the safe site you should perform this du'a during each of the last ten nights of Ramadan. Note that neither al-Mubarakpuri in his commentary on Jami' at-Tirmidhi nor al-Qari his Meshkat detailed on how many times or how or when one should perform this du'a they simply said on this night, as we are recommended to ask Allah while we prostrate it might not be a bad advice to perform it during a prostration in a night prayer or whenever you make a supplication!.
Some reference see here -in Arabic-.