Given two points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ in three dimensional space, the Manhattan distance between those points is defined as
$|x_1-x_2|+|y_1-y_2|+|z_1-z_2|$.

Let $C(r)$ be a sphere with radius $r$ and center in the origin $O(0,0,0)$.
Let $I(r)$ be the set of all points with integer coordinates on the surface of $C(r)$.
Let $S(r)$ be the sum of the Manhattan distances of all elements of $I(r)$ to the origin $O$.

E.g. $S(45)=34518$.

Find $S({10}^{10})$.