  A minimal model for multipole orders in CeB$_6$ shows that degeneracy of the
quadrupole order parameters and strong spin-orbit coupling lead to peculiar
temperature and magnetic-field dependences of the X-ray reflection intensity at
superlattice Bragg points. Furthermore, the intensity depends sensitively on
the surface direction. These theoretical results explain naturally recent X-ray
experiments in phases II and III of CeB$_6$. It is predicted that under weak
magnetic field perpendicular to the (111) surface, the reflection intensity
should change non-monotonically as a function of temperature.
