Can I use a Xbox one Gmail for my Xbox series X

so i have a xbox series x. and i wanted to play a game on it so i buyed a game online on a website but the problem is that the game i buyed was for xbox one and in order to play the game, i am supposed to login in with the xbox one gmail account and i can play the game. so i want to know if i can use a xbox one gmail on my xbox series x so i can play the game saved on that xbox one account that i buyed.

:)