Molecules consisting entirely or predominantly of nitrogen are the focus of much research for their potential as high energy density materials (HEDM). Recent theoretical predictions on cage stability for N-12, N-18, N-24, N-30, and N-36 indicate that the most thermodynamically stable isomer has 3-fold symmetry (D-3h or Dad symmetry point group). Such molecules have a triangle-pentagon bonding group on each end with a band of hexagons around the midsection. However, the existence of this symmetric isomer depends on the number of nitrogen atoms being a multiple of six. In the current study stability trends are addressed for two molecule sizes where this symmetric option does not exist, namely, N-14 and N-16. Isomer energies for these molecules are calculated using Hartree-Fock theory, density functional theory (B3LYP), and perturbation theory (MP4) along with the correlation-consistent basis sets of Dunning. At each molecule size the most stable cage is identified, and the structural features leading to cage stability are discussed.