You can!
You can even listen to the tunes while playing selected games!
Games that support "copied music" include:
Tony Hawk's Pro Skater/Underground (not sure about American Wasteland or Project 8)
Dave Mirra Freestyle BMX 2
Project Gotham Racing (1 and 2)
Steel Battallion: Line of contact
Tetris Worlds (online edition, not sure about offline edition)
There is also a piece of Xbox software around called "Xbox Music Mixer" , of which lets you mix up your copied music
adventure_of_link
I didn't know xbox can rip CDs to the console's hard drive