Extensive semiempirical calculations of the hexaanions of IPR (isolated pentagon rule) and non-IPR isomers Of C-68-C-88 and IPR isomers of C-90-C-98 followed by DFT calculations of the lowest energy structures were performed to find the carbon cages that can provide the most stable isomers Of M3N@C-2n clusterfullerenes (M = Sc, Y) with Y as a model for rare earth ions. DFT calculations of isomers of M3N@C-2n (M = Sc, Y; 2n = 68-98) based on the most stable C-2n(6-) cages were also performed. The lowest energy isomers found by this methodology for Sc3N@C-68, SC3N@C-78, SC3N@C-80, Y3N@C-78, Y3N@C-80, Y3N@C-84, Y3N@C-86, and Y3N@C-88 are those that have been shown to exist by single-crystal X-ray studies as SC3N@C-2, (2n = 68, 78, 80), DY3N@C-80, and Tb3N@C-2n (2n = 80, 84, 86, 88) clusterfullerenes. Reassignment of the carbon cage Of SC2@C-76 to the non-IPR C-s: 17490 isomer is also proposed. The stability of nitride clusterfullerenes was found to correlate well with the stability of the empty 6-fold charged cages. However, the dimensions of the cage in terms of its ability to encapsulate M3N clusters were also found to be an important factor, especially for the medium size cages and the large Y3N cluster. In some cases the most stable structures are based on the different cage isomers for SC3N and Y3N clusters. Up to the cage size Of C-84, non-IPR isomers Of C-2n(6-) and M3N@C-2n were found to compete with or to be even more stable than IPR isomers. However, the number of adjacent pentagon pairs in the most stable non-IPR isomers decreases as cage size increases: the most stable M3N@C-2n isomers have three such pairs for 2n = 68-72, two pairs for n = 74-80, and only one pair for n = 82, 84. For C-86 and C-88 the lowest energy IPR isomers are much more stable than any non-IPR isomer. The trends in the stability of the fullerene isomers and the cluster-cage binding energies are discussed, and general rules for stability of clusterfulerenes are established. Finally, the high yield of M3N@C-80 (l(h)) clusterfullerenes for any metal is explained by the exceptional stability of the C-80(6-) (l(h): 31924) cage, rationalized by the optimum distribution of the pentagons leading to the minimization of the steric strain, and structural similarities of C-80 (l(h): 31924) with the lowest energy non-IPR isomers of C-76(6-), C-78(6-), C-82(6-), and C-84(6-) pointed out.