Generalized Nagaoka ferromagnetism accompanied by flavor-selective Mott states in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>SU</mml:mi> <mml:mo>(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:m

We study the ferromagnetic instability in an SU($N$) Fermi-Hubbard model on the hypercubic lattice. Combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations, we find that, in the strong-coupling regime at low temperatures, ferromagnetically ordered (FM) states develop away from the commensurate fillings. In the particle-doped SU($3$) system near one-third filling, the FM state is accompanied by a spontaneous flavor-selective Mott state, where two of the three flavors are Mott insulating while the remaining flavor is metallic. Since particles in the metallic flavor can almost freely move on the lattice without correlation effects, the ordered state is stabilized by the kinetic-energy gain of the doped particles. This is similar to the generalized Nagaoka ferromagnetism discussed in the one-hole-doped system at one-third filling. In the SU($4$) case, we find that six distinct types of FM states appear as the particle density varies. The results uncover the nature of the FM state in the SU($N$) Fermi-Hubbard systems and highlight the rich magnetic behavior enabled by enlarged internal symmetries.