삼중적분

The midpoint rule for the triple integral $\iiint_{B}f(x,y,z)dV$ over the rectangular solid box $B$ is a generalization of the midpoint rule for double integrals. The region $B$ is divided into subboxes of equal sizes and the integral is approximated by the triple Riemann sum $\sum_{i=1}^{l}\sum_{j=1}^{m}\sum_{k=1}^{n}f\left(\overset{-}{{x}_{i}},\overset{-}{{y}_{j}},\overset{-}{{z}_{k}}\right)\Delta V,$ where $\left(\overset{-}{{x}_{i}},\overset{-}{{y}_{j}},\overset{-}{{z}_{k}}\right)$ is the center of the box ${B}_{ijk}$ and $\Delta V$ is the volume of each subbox. Apply the midpoint rule to approximate $\iiint_{B}{x}^{2}dV$ over the solid $B=\{(x,y,z)|0\le x\le 1,0\le y\le 1,0\le z\le 1\}$ by using a partition of eight cubes of equal size. Round your answer to three decimal places.