How to find the number of spanning trees for a cube? Can you tell me a way of finding the total number of spanning trees in a $Q_d$ undirected labelled graph for $d = 3$. 
I know that the answer is 384, but the way (I know there are many.) of finding it escapes me. 

Extending the answer of Pegah. The eigenvalues of the Laplacian of $Q_d$ are $(0,2,\ldots,2d)$ with respective multiplicities ${d \choose k}.$
Now the product of the nonzero eigenvalues divided by $2^d$ is the number of spanning trees of $G.$ For $d = 3$ we have
$\tau(Q_3) = 2^3 \cdot 4^3 \cdot 6^1/2^3 = 384,$ as confirmed by Juan.
for the lazy ones one can also use Sage math
sage: G = graphs.CubeGraph(3)
sage: G.spanning_trees_count()
384

