8. Let $f(x)=\prod_{i=1}^{4}\left(x^{2}-8 x+c_{i}\right), M=|x|$ $f(x)=0\}$. It is known that $M=\left\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}\right.$, $\left.x_{7}, x_{8}\right\} \subseteq \mathbf{N}$. Then, $\max \left\{c_{1}, c_{2}, c_{3}, c_{4}\right\}-$ $\min \left\{c_{1}, c_{2}, c_{3}, c_{4}\right\}=$ $\qquad$
8.15.

Let the two roots of $x^{2}-8 x+c=0$ be $\alpha, \beta$, then $\alpha+\beta=8$. The unequal non-negative integer values of $(\alpha, \beta)$ are only $(0,8),(1,7),(2,6)$, $(3,5)$. Therefore, $\left\{c_{1}, c_{2}, c_{3}, c_{4}\right\}=\{0,7,12,15\}$.