Cubic GaN samples on GaAs(0 0 1) substrates were grown by RF-plasma-Assisted molecular beam epitaxy (RF-MBE), an As4 overpressure was employed during the nucleating layer. We found that the relaxation process of c-GaN during the nucleating layer, affects the purity of cubic phase. Higher cubic phase of GaN was obtained for samples that initiated the relaxation process after some monolayers (8ML) of growth, as a result of better stabilization of the cubic layer. The relaxation process depends on the As4 overpressure over the growth surface and on the growth temperature. The structural properties of c-GaN characterized by transmission electron microscopy (TEM) and high resolution X-ray diffraction (HR-XRD) have evidenced the purity of cubic phase in the first nanometer of growth, and also the formation of the hexagonal inclusions after several nanometers of growth from the stacking faults on the {1 1 1} planes. From an estimation of the hexagonal content by X-ray reciprocal space mapping (RSM), we found a lower hexagonal component on the (11¯1)N and (1¯11)N planes. The highest purity of cubic GaN was 98.7% along the {1 1 1}N planes for sample grown at 720°C. Photoluminescence measurements also demonstrated the high purity of the cubic phase of this sample, no emission of hexagonal inclusion was detected.