If you are playing an original backwards compatible Xbox game on the Xbox 360 you may run into a problem because the Xbox 360 controller, unlike the original Xbox controller or the controller S, does not have the black or white buttons.
This means that entering cheat codes, or using the black and white buttons for any function has to use the new controller layout.
Microsoft thought of this when they designed the Xbox 360 controller and have replaced the Black and White buttons with the Right and Left Bumpers. Specifically, here are what bumper buttons replace the Black and White buttons:
Left Bumper replaces the White button. (#3 on image above)
Right Bumper replaces the Black button. (#4 on image above)
So if a cheat code was Left, A, Black, X, White, B, B on the Xbox, it would be Left, A, Right Bumper, X, Left Bumper, B, B while playing the same game on the Xbox 360.
For all backwards compatible Xbox games on the Xbox 360 this replacement method should be used to correctly control the game and enter cheat codes.