Question 6
Let $m \neq 0$ be an integer. Find all polynomials $P(x)$ with real coefficients such that
$$
\left(x^{3}-m x^{2}+1\right) P(x+1)+\left(x^{3}+m x^{2}+1\right) P(x-1)=2\left(x^{3}-m x+1\right) P(x)
$$
for all real numbers $x$.
$$
\left(x^{3}-m x^{2}+1\right) P(x+1)+\left(x^{3}+m x^{2}+1\right) P(x-1)=2\left(x^{3}-m x+1\right) P(x)
$$
for all real numbers $x$.