The structural and electrical properties of Mg-doped cubic GaN epi-layers grown by plasma-assisted molecular beam epitaxy (PAMBE) near Ga rich conditions are investigated. The diffraction of high-energy reflected electrons (RHEED) in situ, in addition to structural studies of X-ray diffraction, show that the fraction of hexagonal and crystal twinning inclusions decreases when the Mg flux increases. The condition for the higher incorporation of Mg where the electrical properties are optimized is highly sensitive to the flow ratio Mg/Ga. The p-doping level steadily increases with increasing Mg flux. The Mg concentration obtained by secondary ion mass spectroscopy (SIMS) from samples grown at Mg temperatures from 200 °C to 700 °C are in a range between 2 × 1019 to 2 × 1020 atoms/cm3. The highest mobility and p-type doping level achieved, determined from Hall measurements, were 28.2 cm2/V-s and 2 × 1019 cm−3, respectively. We corroborate that the Mg doped c-GaN films are suitable for the construction of optoelectronic devices based on cubic III-Nitrides.