Compute the expected value of $W^3$, i.e. $\mathbb E(W^3)$

Question

My problem:

Let $X_1,...,X_n$ be a random sample from a $\mathsf{Normal}(\mu_1,\sigma^2$) distribution and $Y_1,...,Y_m$ be a random sample from a $\mathsf{Normal}(\mu_2,\sigma^2$) distribution, independent with $X_1,...,X_n$.

Define: $W =\frac1n\sum_{i=1}^n(X_i −\overline X_n)^2$

problem (c).

Compute the expected value of $W^3$, i.e. $\mathbb E(W^3)$.

How should I solve this problem?