Show that $E[ N^T C N N^T]=0$ where $N \in \mathbb{R}^n$ be a zero-mean Gaussian vector with covariance matrix $\Sigma$

Question

Let $N \in \mathbb{R}^n$ be a zero-mean Gaussian vector with covariance matrix $\Sigma$. I am trying to compute \begin{align} E[ N^T C N N^T] \end{align} where $C$ is $n \times n$ symetric positive-definite matrix.

What I tried: In the scalar case, this is zero because we get $CE[N^3]=0$. I also tried a $2 \times 2$ example and it is zero there as well.