While looking for a closed form of a expression I worked myself to a formula that resembles the Vandermonde convolution, but is summed over even binomial coefficients only.

$\sum_{k=0}^n\sum_{l=0}^n{{2k+2l}\choose{2l}}{{4n-2k-2l}\choose{2n-2l}}$

I'm at a loss as to what to do with it. I can re-write it in several ways, but the principal problem remains. Is there a known technique to attack such sums? Thanks.