8. Given $1 \leqslant x, y, z \leqslant 6$.

The number of cases where the product of the positive integers $x, y, z$ is divisible by 10 is
$\qquad$ kinds.
8. 72 .
(1) The number of ways to choose $x, y, z$ is $6^{3}$;
(2) The number of ways to choose $x, y, z$ without taking $2, 4, 6$ is $3^{3}$; (3) The number of ways to choose $x, y, z$ without taking 5 is $5^{3}$;
(4) The number of ways to choose $x, y, z$ without taking $2, 4, 5, 6$ is $2^{3}$. Therefore, the number of ways for the product of $x, y, z$ to be divisible by 10 is $6^{3}-3^{3}-5^{3}+2^{3}=72$.