Mean squared error of MLE of $\theta$ where $f(x) = 3 \theta e^{-\theta x^3} 1_{(0,\infty)}(x)$

Given $f(x) = 3 \theta e^{-\theta x^3} 1_{(0,\infty)}(x)$ I want to find the MSE of the MLE estimator for $\theta$. I've found that $\hat{\theta} = \frac{n}{\sum_{i=1}^n X_i^3} = \frac{1}{\bar{X^3}}$.

I know that $MSE(\hat{\theta}) = Var(\hat{\theta}) + Bias(\hat{\theta})^2$ but I am having trouble finding $E(\hat{\theta})$ and $E(\hat{\theta}^2)$ here. How should I proceed?