8. $(1, \sqrt[3]{4}]$.

Let $u=a+b$.
Then $u>0$, and $a=u-b(00
\end{array} \Leftrightarrow 1<u \leqslant \sqrt[3]{4} .\right.
$

Therefore, the range of values for $a+b$ is $(1, \sqrt[3]{4}]$.
8. Given $a>0, b>0, a^{3}+b^{3}=1$. Then the range of $a+b$ is . $\qquad$