2. Let real numbers $a, b$ satisfy:
$$
a^{3}-3 a b^{2}=39, b^{3}-3 a^{2} b=26 \text {. }
$$

Then the value of $a^{2}+b^{2}$ is $\qquad$
2. 13.
$$
\begin{array}{l}
\text { Given } 39^{2}+26^{2}=\left(a^{3}-3 a b^{2}\right)^{2}+\left(b^{3}-3 a^{2} b\right)^{2} \\
=\left(a^{2}+b^{2}\right)^{3} \\
\Rightarrow a^{2}+b^{2}=13 .
\end{array}
$$