Understanding superatom molecular orbital (SAMO) states in fullerene derivatives has been in the limelight ever since the first discovery of SAMOs owing to the fundamental interest in this topic as well as to the possible applications in molecular switches and other organic electronics. Nevertheless, very few reports have been published on SAMO states of larger fullerenes so far. Using density functional theory, we attempt to partially remedy this situation by presenting a study on SAMO states in C82 and its Ca and Sc endohedrally doped derivatives, comparing results with previous relevant findings for C60. We find that C82 possesses higher SAMO energies compared to C60, as associated with the symmetry of the molecule, and that endohedral doping leads to energetically favorable side positions of Ca and Sc inside the C82 cage. Among the two, Sc@C82 has more stable SAMO states compared to Ca@C82 as reflected by the shift in the density of states, while the charge states are found to be similar. In the case of the monolayer form, the pz- and 2s-SAMO orbitals overlap with the nearest neighbors, causing parabolic band dispersion with the formation of near free electron states and that the SAMO state energies move closer to the Fermi energy compared to the related molecules. These findings provide promising information about the distribution of SAMO states in C82 fullerene, which can be further relevant in studies of SAMO states of higher fullerenes and for coming applications of these systems.