A computational study on the experimentally detected Sc3N@C-68 cluster is reported, involving quantum chemical analysis at the B3LYP/6-31G* level. Extensive computations were carried out on the pure C-68 cage which does not conform with the isolated pentagon rule (IPR). The two maximally stable C68 isomers were selected as initial SC3N@C-68 cage structures. Full geometry optimization leads to a confirmation of an earlier assessment of the Sc3N@C-68 equilibrium geometry (Nature 2000, 408, 427), namely an eclipsed arrangement of Sc3N in the C-68 6140 frame, where each Sc atom interacts with one pentagon pair. From a variety of theoretical procedures, a D-3h structure is proposed for the free Sc3N molecule. Encapsulated into the C-68 enclosure, this unit is strongly stabilized with respect to rotation within the cage. The complexation energy of Sc3N@C-68 cage is found to be in the order of that determined for Sc3N@C-80 and exceeding the complexation energy of Sc3N@C-78. The cage-core interaction is investigated in terms of electron transfer from the encapsulated trimetallic cluster to the fullerene as well as hybridization between these two subsystems. The stabilization mechanism of Sc3N@C-68 is seen to be analogous to that operative in Sc3N@C-78. For both cages, C-68 and C-78, inclusion of Sc3N induces aromaticity of the cluster as a whole.