8. Let $\left(1+x+x^{2}\right)^{150}=\sum_{k=0}^{300} c_{k} x^{k}$, where $c_{0}$, $c_{1}, \cdots, c_{300}$ are constants. Then $\sum_{k=0}^{100} c_{3 k}=$ $\qquad$ .
$8.3^{149}$.
Notice that,
$$
\begin{array}{l}
\left(1+x+x^{2}\right)^{150}=\left(1+x+x^{2}\right)\left(1+x+x^{2}\right)^{149} \\
=\left(1+x+x^{2}\right) \sum_{k=0}^{298} d_{k} x^{k} .
\end{array}
$$

Let $x=1$. Then
$$
3^{150}=3 \sum_{k=0}^{100} c_{3 k} \Rightarrow \sum_{k=0}^{100} c_{3 k}=3^{149} .
$$