$(30$ points$)$ Consider the vector field

$F(x,y,z)=x^{3}i+y^{3}j+z^{3}k$

By use of the Divergence Theorem, evaluate the outward flux of $F$

$I={}_{S}F*dS$

where $S$ is the boundary of the cube $E$ with vertices at $(0,0,0),(1,0,0),(0,1,0),(1,1,0),(0,0,1),(1,0,1),(0,1,1)$ and $(1,1,1),$ with normal vector directed outward from $E.$