Using the modified analytic embedded atom method and molecular dynamics, the binding energies and their second order finite differences stability functionsd of icosahedral Ni clusters with shell and subshell periodicity are studied in detail via atomic evolution. The results exhibit shell and sub shell structures of the clusters with atoms from 147 to 250 000, and the atomic numbers corresponding to shell or subshell structures are in good agreement with the experimental magic numbers obtained in time-of-flight mass spectra of threshold photoionization, and Martin’s theoretical proposition of progressive formation of atomic umbrellas. Clusters with size from 147 to 561 atoms are energetically investigated via one-by-one atomic evolution and their magic numbers are theoretically proved. For medium-size Ni clusters with 561 to 2057 atoms, the prediction of magic numbers with atomic numbers is performed on the basis of umbrellalike subshell growth in near face-edge-vertex order. The similarity of the energy curves makes it possible to extend the prediction to even larger Ni nanoclusters in hierarchical Mackay icosahedral configurations.