The relative stabilities of nonisomers are investigated. Twenty-two species of nitrogen cage molecules N(2n) (N6 (D(3h)), N8 (Oh), N10 (D(5h)), N12 (D(6h)), N12 (D(3d)), N16 (D(4d)), N18 (D(3h)), N20 (Ih), N24 (D(3d)), N24 (D(4h)), N24 (D(6d)), N30 (D(3h)), N30 (D(5h)), N32 (D(4d)), N36 (D(3d)), N40 (D(4h)), N42 (D(3h)), N48 (D(4d)), N48 (D(3d)), N54 (D(3h)), N56 (D(4h)), and N60 (D(3d))), which are divided into four sets, have been studied in detail. The geometries and varieties of energies are examined extensively, and NBO analysis and AIM analysis are applied to investigate the bonding properties of the cage molecules. The introducing of the concept of "layer" can well assist in explaining why one nonisomer molecule is more stable than another one. The results show that the lengths of bonds, on both sides of which are five-membered rings (referred to as pentagons), are the shortest and the orbital energies are the lowest. The nonlocalized electron numbers of orbitals, on at least one side of which is a triangle, are the greatest. Pentagons play a major role in the stability of a cage molecule, and the three-membered rings (referred to as triangles) play the second one. The layers in nitrogen cage molecules also contribute to the relative stabilities.