For the vector field vec$(E)=$hat$(x)6x{y}^3+$hat$(y)5y^3{z}^2-$hat$(z)4x{z}^2,$ verify the divergence theorem by computing:

a$)$ The total outward flux $o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$vec$(E)*dvec(S)$ flowing through the surface of a cube centered at the origin and with sides equal to $2$ units each and parallel to the Cartesian axes. $($namely$,-1x1,-1y1,$ and $-1z1)$

b$)$ The integral of grad$*vec(E)$ over the cube's volume. $($Double check your result by comparing with results in $($a$))$