  We calculate the resonant x-ray scattering (RXS) spectra near the Ce $L_{\rm
III}$ absorption edge in CeB$_6$, on the basis of a microscopic model that the
$4f$ states of Ce are atomic while the $5d$ states form an energy band with a
reasonable density of states. In the initial state, we employ an effective
Hamiltonian of Shiina {\it et al}. in the antiferro-quadrupole (AFQ) ordering
phase, while we construct the wave function consistent with the neutron
scattering experiment in the magnetic ground state. In the intermediate state,
we take full account of the intra-atomic Coulomb interaction. Without assuming
any lattice distortion, we obtain sufficient RXS intensities on the AFQ
superlattice spot. We obtain the spectral shape, the temperature and magnetic
field dependences in good agreement with the experiment, thus demonstrating the
mechanism that the intensity is brought about by the modulation of $5d$ states
through the anisotropic term of the $5d$-$4f$ Coulomb interaction. In the
magnetic ground state, a small pre-edge peak is found by the $E_2$ process. On
the magnetic superlattice spot, we get a finite but considerably small
intensity. The magnetic form factor is briefly discussed.
