Question 181
Find all integers $n$ such that there exists a polynomial $P(x)$ with integer coefficients satisfying
$$
P\left(\sqrt[3]{n^{2}}+\sqrt[3]{n}\right)=2016 n+20 \sqrt[3]{n^{2}}+16 \sqrt[3]{n} .
$$
$$
P\left(\sqrt[3]{n^{2}}+\sqrt[3]{n}\right)=2016 n+20 \sqrt[3]{n^{2}}+16 \sqrt[3]{n} .
$$