Not 1 or 2 but 3 Integrals

Number Theory and Algebra Level pending

What is $\int \int \int_B xyz^2\ dV,$ where $B$ is the cuboid bounded by the regions $0 \leq x \leq 1$ , $-1 \leq y \leq 2$ and $0 \leq z \leq 3?$