8. Given $a>0, b>0, a^{3}+b^{3}=1$. Then the range of $a+b$ is $\qquad$

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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. \text {. }
$$

Therefore, the range of values for $a+b$ is $(1, \sqrt[3]{4}]$.