1. Given $a=\frac{1}{2+\sqrt{7}}, b=\frac{1}{2-\sqrt{7}}$. Then $a^{3}-a+b^{3}-b=$ $\qquad$ .
-1. $-\frac{64}{27}$.
$$
\begin{array}{l}
\text { Note that, } a+b=-\frac{4}{3}, a b=-\frac{1}{3} . \\
\text { Therefore, the original expression }=\left(a^{3}+b^{3}\right)-(a+b) \\
=(a+b)\left(a^{2}-a b+b^{2}-1\right) \\
=(a+b)\left[(a+b)^{2}-3 a b-1\right] \\
=\left(-\frac{4}{3}\right)\left(\frac{16}{9}+1-1\right)=-\frac{64}{27} .
\end{array}
$$