  Let $\tau_3(n)$ be the triple divisor function which is the number of
solutions of the equation $d_1d_2d_3=n$ in natural numbers. It is shown that $$
\sum_{1\leq n_1,n_2,n_3\leq
\sqrt{x}}\tau_3(n_1^2+n_2^2+n_3^2)=c_1x^{\frac{3}{2}}(\log x)^2+
c_2x^{\frac{3}{2}}\log x +c_3x^{\frac{3}{2}}
+O_{\varepsilon}(x^{\frac{11}{8}+\varepsilon}) $$ for some constants $c_1$,
$c_2$ and $c_3$.
