Answer

The M3's have a locking differential that makes a lot of noise, especially in the break in period. The noise tends to get better as the car breaks in, but still can be audible especially if you know what you are listening for. Some thing you can try is find a parking lot where you can do a lot of circles. I would go one direction for about 10 turns, then the other for about 10 turns. Maybe even do this procedure more than once to see if it helps the noise. If this does not work, or it does not get to quiet enough standards their might be a special oil that you can put in your differential depending on the producting month of you car (this can be found on a black sticker in the drivers side door pilar). If you give me the month and the miles on the car I could recommend this oil change for you.

Another thing you may consider is the rear tire tread depth (or if on side tire is flat out a different size than the other). If on side tire is bald and the other is pretty new than the locking differential will slip more in a turn, than it is supposed to, and make the noise you hear of.

If you found my information helpful please click accept! If you have any more questions regarding this issue, do not hesitate to ask. Good feedback also helps me out!