The electrochemistry of three new clusterfullerenes Dy3N@C2n (2n=78, 80), namely two isomers of Dy3N@C80 (I and II) as well as Dy3N@C78 (II), have been studied systematically including their redox-reaction mechanism. The cyclic voltammogram of Dy3N@C80 (I) (Ih) exhibits two electrochemically irreversible but chemically reversible reduction steps and one reversible oxidation step. Such a redox pattern is quite different from that of Sc3N@C80 (I), and this can be understood by considering the difference in the charge transfer from the encaged cluster to the cage. A double-square reaction scheme is proposed to explain the observed redox-reaction behavior, which involves the charge-induced reversible rearrangement of the Dy3N@C80 (I) monoanion. The first oxidation potential of Dy3N@C80 (II) (D5h) has a negative shift of 290 mV relative to that of Dy3N@C80 (I) (Ih), indicating that lowering the molecular symmetry of the clusterfullerene cage results in a prominent increase in the electron-donating property. The first and second reduction potentials of Dy3N@C78 (II) are negatively shifted relative to those of Dy3N@C80 (I, II), pointing to the former's lowered electron-accepting ability. The significant difference in the electrochemical energy gaps of Dy3N@C80 (I), Dy3N@C80 (II), and Dy3N@C78 (II) is consistent with the difference in their optical energy gaps.