8. Given the set of lattice points $S=\{(x, y) \mid x, y \in\{0,1,2,3,4,5\}\}$, find the number of triangles with vertices in $S$.
8. The number of triangles with vertices at the lattice points in $S$ is: $C_{36}^{3}-12 \cdot C_{6}^{3}-100-32=6768$.