  We study algebras with a distributive law and the Koszulness of associated
operads. As a corollary of our theory we prove that the homology operad of the
little cubes operad is Koszul, the result which was originally proven by E.
Getzler and J.D.S. Jones in their preprint "Operads, homotopy algebra, and
iterated integrals for double loop spaces" using the combinatorics of the
stratification of the Fulton-MacPherson compactification of the configuration
space. Since the above mentioned result whose purely algebraic proof we give
plays and important role in closed string field theory and especially the
methods used in the original proof of Getzler and Jones are very relevant for
this part of mathematical physics, we decided to put our paper here, though
some 80% of its material belongs rather to universal and homological algebra.
