I want to compute the following expectation term:

$E[{\bf{XA}}{{\bf{X}}^T}]$

where ${\bf X} \in R^{M \times M}$ and its elements are normal random variables such that

$vec\left( {\bf{X}} \right)\sim \cal N\left( {\boldsymbol \mu ,\bf \Sigma } \right)$

$\bf A$ is a positive definite matrix with proper dimensions and $vec(.)$ is the vectorization operator. Any hint on how I can derive a nice formula?