Cubic GaN was grown on 6H-SiC(0001) by electron-cyclotron resonance plasma-assisted molecular-beam epitaxy. The growth process consisted of first depositing a 20-nm GaN buffer, followed by ten periods of alternating layers of 1 monolayer (ML) Mn and 10 ML GaN, and finally capped with 30 nm GaN. High-resolution transmission electron micrographs of film cross sections were recorded and digital diffractograms were calculated to determine the lattice structures of the different film layers. It was found that the crystal structure in the GaN buffer and capping layer matches the 2H-wurtzite GaN. However, uniform cubic zinc-blende GaN phase was observed in place of the nominal multilayer Mn/GaN region. The density of defects typically observed in GaN films is drastically reduced within the cubic and capping layer, indicating improved film quality possibly due to the surfactant effect of Mn. Based on the one-dimensional Ising model of polytype formation, a mechanism is proposed to explain the growth of cubic GaN in the Mn/GaN region.