Anticommutator Green’s functions and energy spectra of fullerene C26 and endohedral fullerene U@C26 with the D3h symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation ap-proximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecules C26 and U@C26 with the D3h symmetry groups have been determined.