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In this study, the stabilization energies of the nH2@BmNm complexes (m = 12, 24, 36, 48, 60) have been determined by exploiting several density functional theory methods, namely B3LYP, PBE1PBE and ωB97X-D. Among these density functional theory methods, ωB97X-D is found to be the most appropriate for the systems involving H2 doping in boron nitride nanocages. It predicted that the smallest nanocage, B12N12, has no stable complex and the H2@B24N24, 2H2@B36N36, 4H2@B48N48 and 7H2@B60N60 complexes are the most stable hydrogenboron nitride complexes. Accordingly, it is found that the number of hydrogen molecules doped inside the most stable complex of each nanocage quadratically depends on nanocage size. This indicates that as the size of nanocage, as well as, the size of the endohedral cavity increases more stable nH2@BmNm complexes are formed.