it's the rear diff locking on tight turns, it causes a rumbling sort of noise.
There is a "fix" for it from BMW. It's bassically rear diff oil with an "FM Booster (Friction Modifier). Anyway it's called SAF-XJ+FM Booster.
Add that, then find a nice big empty space and do 9x tight turns left, and 9x tight turns right to circulate the fluid through it.
I had the same issue, took it in for a service and got the diff oil changed, decided to try it on the standard oil for an M3 and it's improved it but it still does it on occasion.
HTH.
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Monte Carlo Blue M3 Comp
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