Original cube side length is s = 4 inches, so the vol. is 4^3 in^3, or 64 in^3 = s^3.
If we double the original side length, we get S = 2s, and the new volume
is S^3 = (2s)^3 = 8s^3 = 8(64 in^3) = 512 in^3.
Answer: the new cube has a volume 8 times greater than the original cube has.