Answer
$4a(a+b)(a-b)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here by deducing the volume of the smaller one from the big one: $V=4a^3-4ab^2=4a(a^2-b^2)=4a(a+b)(a-b)$