The C4nH2nN2n (n = 3-8) cage molecules with D,,,, symmetry and their nitrated products, C4nN4nO4n (11 = 3, 4, 5) and C4nHnN3nO2n (n = 4, 6, 8) were studied by DFT at the B3LYP/cc-pVDZ level. Their geometrical structures, ground-state energies, and heats of formation have been investigated. The), exhibit an obvious cage effect. Hirshfeld partitioning charges in momentum space give evidence of high strained energy in the title compounds. Their orbital energy and frontier orbital shape and electrostatic potential Calculation are also studied. Investigation of heat of formation and NICS analysis reveal that C24H12N12 is the most stable molecule among title compounds with D-nh symmetry. Their half nitrated products are predicted as a promising candidate for high energy matter.