Determinants, Pfaffians, and...?

Question

I recently stumbled across the wikipedia entry on Pfaffians and found them rather interesting, especially the property below. (assuming $A$ is a $2n\times 2n$ skew symmetric matrix) $$\det(A)=\mbox{pf}(A)^2$$ This got me thinking, does this go to higher powers? Is there such a determinant/Pfaffian type object with the following property? $$\det(B)=\mbox{f}(B)^3$$