Let $\varphi (x)$ be a smooth function supported on $[1,2]$ with derivatives bounded by ${\varphi }^{(j)}(x)\ll 1$ and $d_3(n)$ be the number of ways to write $n$ as a product of three factors. We get the asymptotic formula for the nonlinear exponential sum $\sum _{n\equiv lmodq}{d}_3(n)\varphi \left(\frac{n}{X}\right)e\left(\frac{3\sqrt[3]{kn}}{q}\right)$.