My rear quick release made the same noise. It only happened when pushing hard on the pedals. I was so sure it was the bottom bracket!

I cleaned the external cam on the quick release, wiped the frame where it clamped, and tightened the clamp a little more than I did originally. Fixed. I have to do this every couple of months.

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The other common cause is at the crankarm - crank axle splines, if it's one of those two-bolt style attachments. It's normally fixed by wiping off the splines, then greasing them before reassembly.