Cubic GaN films were grown on GaAs substrates by plasma-assisted molecular beam epitaxy (MBE). Using real-time control of the group V/III flux ratio by means of RHEED, single-phase cubic GaN films with superior structural and optical properties were obtained. A narrow excitonic luminescence line at 3.272 eV is observed at 5 K, yielding a low-temperature energy gap of 3.30 eV. The nucleation of the metastable cubic GaN phase with a well-defined orientation relationship to the GaAs substrate is discussed. In addition, we discuss the origin of the n-type background doping in the as-grown layers, and we present a new concept of codoping to achieve high p-type conductivity in GaN at room temperature.