i did not get zero, and you should not either. this integral is giving the volume of a solid. it gives the volume of the region in the first octant bounded between a sphere of radius 1 and a sphere of radius 2, both centered at the origin.
Think of this. Everything from the outside to the grey thing. Except in this solid it is 1/2 the size of semi-earth. So divide that shape into two equal part to get your solid.