it does play CDRW, but it will not play CDRs, so, taken right from i site i write for -

Playing burned music discs

Burn music onto a CD-RW (not a CD-R) disc, and close the session when you burn the CD. Place it in your X-Box and rip it. Note: This also works with .MP3 files. The Xbox can store .MP3s and replay them later and saves a lot of space when compared to the .WAV files that are standard on audio discs.

i still need to test this, to see if it works