It sounds like a bad u-joint. Check the drive shaft for extra play around the u-joints. The one next to the rear end is more than likely bad.

Rear axle bearing failure or differential. Has anyone ever bothered to see if any oil is left in the axle?

so it just ended up being a loose rear diff pinion bearing

Diff or half shaft bearings on verge of collapsing.

When I am driving an I take my foot off of the gas to coast or I hit the brake the car makes a loud humming noise coming from the back. It doesn't feel any different in power an the second I hit the gas the noise goes away until I take my foot off the gas again. I drive a v6 Pontiac firebird with auto trans ..plz help I do not know what this noise is