Cubic III-nitrides are attractive for optoelectronic applications, thanks to the absence of the giant internal electric field (several MV/cm) characteristic of hexagonal heterostructures. The growth of cubic GaN on AlN is performed by plasma assisted molecular beam epitaxy on pseudosubstrates consisting of 3 mum-thick 3C-SiC grown on Si(001) by atmospheric pressure chemical vapour deposition. We study the Ga coverage on GaN in order to optimize the growth of GaN on SiC. We demonstrate that the Ga behaves as a surfactant on GaN for a certain range of Ga fluxes and substrate temperatures. The influence of this Ga film present on the growing surface is discussed for the growth of GaN quantum dots on AlN. It is a key parameter for the value of the critical thickness at which the 2D-GaN strained layer relaxes by forming three-dimensional islands.