We have studied the Mg doping of cubic GaN grown by plasma-assisted Molecular Beam Epitaxy (PA-MBE) over GaAs (001) substrates. In particular, we concentrated on conditions to obtain heavy p-type doping to achieve low resistance films which can be used in bipolar devices. We simulated the Mg-doped GaN transport properties by density functional theory (DFT) to compare with the experimental data. Mg-doped GaN cubic epitaxial layers grown under optimized conditions show a free hole carrier concentration with a maximum value of 6 × 1019 cm−3 and mobility of 3 cm2/Vs. Deep level transient spectroscopy shows the presence of a trap with an activation energy of 114 meV presumably associated with nitrogen vacancies, which could be the cause for the observed self-compensation behavior in heavily Mg-doped GaN involving Mg-VN complexes. Furthermore, valence band analysis by X-ray photoelectron spectroscopy and photoluminescence spectroscopy revealed an Mg ionization energy of about 100 meV, which agrees quite well with the value of 99.6 meV obtained by DFT. Our results show that the cubic phase is a suitable alternative to generate a high free hole carrier concentration for GaN.