(Co-) Homology of free nilpotent Lie Algebras

What is actually known about the (co-) homology of free nilpotent Lie Algebras over $\mathbb{C}$ and coefficients also in $\mathbb{C}$? I.e. the nilpotent Lie Algebras that one gets by a quotient of a free Lie algebra by some part of its descending central series.