Endohedral metallofullerenes (EMFs) with a trapped cluster size larger than four are rather scarce. Inspired by a recent experimental observation, we explored the possibility of encapsulating an unusual Sc₃NC unit in three representative fullerene cages, namely, C₆₈, C₇₈ and C₈₀, by means of density functional computations. The geometries, electronic and electrochemical redox properties of the corresponding EMFs, Sc₃NC@C_2n (2n = 68, 78 and 80), were investigated. These novel EMFs all have very favorable binding energies, implying a considerable possibility for experimental realization. The recently observed m/z = 1121 peak in the mass spectroscopy was characterized as Sc₃NC@C₈₀. Notably the lowest-energy isomer of Sc₃NC@C₇₈ has a non-IPR C₇₈ outer cage, the possibility to accommodate five atoms inside a fullerene as small as C₆₈ is also intriguing. Moreover, the intracluster and metal-cage covalent interactions were revealed by a quantum theory of atoms in molecules study. Infrared absorption spectra and ¹³C nuclear magnetic resonance spectra were also computed to assist future experimental characterization.