8. Given a fifth-degree polynomial $f(x)$ with the leading coefficient of 1 satisfies: $f(n)=8 n, n=1,2, \cdots, 5$, then the coefficient of the linear term of $f(x)$ is $\qquad$ .
According to the problem, $f(x)=(x-1)(x-2)(x-3)(x-4)(x-5)+8 x$, so its coefficient of the linear term is $5!\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)+8=120+60+40+30+24+8=282$