$$m^{3}+2p^{3}=3mn$$
$\left\{\begin{matrix}n=\frac{m^{3}+2p^{3}}{3m}\text{, }&m\neq 0\\n\in \mathrm{R}\text{, }&m=0\text{ and }p=0\end{matrix}\right.$
$$3mn=m^{3}+2p^{3}$$
$$\frac{3mn}{3m}=\frac{m^{3}+2p^{3}}{3m}$$
$$n=\frac{m^{3}+2p^{3}}{3m}$$
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