The cubic phase of boron nitride (c-BN) is an extremely promising multifunctional material. However, to exploit all possible applications, a successful route for large area chemical vapor deposition (CVD) of c-BN films is required. Adsorption of gaseous growth species onto the c-BN surface is one of the key elementary reactions in CVD growth of c-BN. In the present work, the ability of BHx, BFx, and NHx species (x = 0, 1, 2, 3) to act as growth species for CVD of c-BN, in an H-, F-, or H/F-saturated gas-phase, has been investigated using density functional theory (DFT) calculations. It was found that the most optimal growth species for CVD growth of c-BN are B, BH, BH2, BF, BF2, N, NH, and NH2 in an H/F-saturated gas-phase, i.e., decomposition of the incoming BH3, BF3, and NH3 growth species is very crucial for CVD growth of c-BN. It was also found that it would be most preferable to use a CVD method where the incoming BH3, BF3, and NH3 growth species are separately introduced into the reactor, e.g., by using an atomic layer deposition (ALD) type of method.