Floyd Mayweather -- Hardcore Gym Training ... to JUSTIN BIEBER Music

When Floyd Mayweather hits the gym, it's important to listen to music that makes him wanna DESTROY people in the ring -- which could be why he likes to rock out to Justin Bieber.

Bieber just posted footage of Floyd hard at work at his boxing gym, knocking out an ab routine to Justin's track "Right Here (featuring Drake)."

Justin also posted a note with the clip saying, "The champ @floydmayweather training to my music . Atta boy."