The paper is concerned with hexacyclic systems (\( F_n \)) and their Möbious counterparts (\( M_n \)). Continuing the studies in MATCH Commun. Math. Comput. Chem. 94 (2025) 477, the characteristic polynomial and the eigenvalues of the Sombor matrix of \( F_n \) and \( M_n \), and the respective Sombor energies are determined. Upper and lower bounds for the Sombor energy in terms of the number of hexagons are also obtained.