The drum-like C4nN2n (n = 3-8) cages and corresponding hydrogenated products C4nH4nN2n, (n = 3-8) are studied at the DFT B3LYP/6-31G** level. Their structures, energies, and vibrational frequencies have been investigated. Comparison of heat of formation reveals that C32N16 with D-8h symmetry in the C4nN2n (n = 3-8) series is a promising candidate as high energy density matter. The calculation of the Delta G and Delta H for the hydrogenation of C4nN2n (n = 3-8) shows that it is; an exothermic reaction at 298 K and the C4nH4nN2n (n = 3-8) species are more stable than C4nN2n (n = 3-8) species. The analysis of molecular orbital and selected bond lengths of N-N and C-C provides another insight about their stability. Combined with the nucleus-independent chemical shifts (NICS) calculation, it is indicated that molecular stability for cage-shaped molecules depends on not only aromatic character but also the cage effect.