8. The function $f(x)$ is defined on $\mathbf{R}$, and for any real number $x$, it holds that $f(1+x)=f(3-x)$, and $f(2+x)=$ $-f(4-x)$, find the value of $f(1)+f(2)+\cdots+f(100)$.
8. For any real number $x$, the function $f(x)$ satisfies $f(1+x)=f(3-x)$ and $f(2+x)=-f(4-x)$. This means $f(x)$ is a generalized (II) type even function with respect to the real numbers $1$ and $3$, and a generalized (II) type odd function with respect to the real numbers $2$ and $4$. Therefore, $2|(1+3)-(2+4)|=4$ is one of its positive periods.
$f(1)=f(3-2)=f(1+2)=f(3)=f(2+1)=-f(4-1)=-f(3), f(2)=-f(4)$, which implies $f(1)+f(3)=0, f(2)+f(4)=0$. Thus, $f(1)+f(2)+\cdots+f(100)=25[f(1)+f(2)+f(3)+f(4)]=0$.