Diophantine Equations · Challenge problem

Squares are $0, 1, 4 \pmod 8$. Using this (and the fact that every $n \le 100$ not ruled out by such an argument really is a sum of three squares), find how many integers $n$ with $1 \le n \le 100$ are not of the form $x^2 + y^2 + z^2$ with integers $x, y, z$.