To accurately predict the enthalpies of formation of all-nitrogen materials, nine density functionals including B3PW91, B3P86, B3LYP, X3LYP, O3LYP, M052X, M062X, M06HF, B2PLYP52 were employed to calculate the enthalpies of formation of nitrogen-rich compounds via atomization reaction. The calculation results show that double hybrid functional B2PLYP has the smallest mean absolute deviation of 30.1 kJ·mol^-1, which is more accurate than G4 method. Hence, the enthalpies of formation of five all-nitrogen molecules with cage structure, namely, N₄(T_d), N₆(D_3h), N₈(O_h), N₁₀(D_5h), and N₁₂(D_6h), were predicted by B2PLYP functional, and the corresponding results were 756.4, 1338.2, 1878.5, 2144.3, 2787.0 kJ·mol^-1, respectively.