  We consider scalar field perturbations of the asymptotically G\"odel
5-dimensional charged rotating black holes with two equal angular momenta. It
is shown that the spectrum of proper oscillations of the perturbation includes
superradiant unstable modes. The reason for the instability is the confining
Dirichlet boundary condition at the asymptotically far region of the G\"odel
Universe. The confining box makes superradiant modes extract rotational energy
from the black hole and, after repeated reflections from the black hole, grow
unboundedly. A similar instability takes place for rotating black holes in the
asymptotically anti-de Sitter (AdS) space-time.
