6 The number of tetrahedra with vertices at the vertices of the cube $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ is
658 Prompt: From the 8 vertices of a cube, any four points can be chosen, with $\mathrm{C}_{8}^{4}=70$ (ways) of selection. Removing the 6 faces and 6 diagonal planes, we get 58 tetrahedra.