Rare-earth hexaborides have attracted a considerable attention recently in connection to variety of correlated phenomena including heavy fermions, superconductivity and low temperature magnetic phases. Here, we present high-resolution angle-resolved photoemission spectroscopy studies of trivalent CeB 6 and divalent BaB 6 rare-earth hexaborides. We find that the Fermi surface electronic structure of CeB 6 consists of large oval-shaped pockets around the X points of the Brillouin zone, while the states around the zone center Γ point are strongly renormalized. Our first-principles calculations agree with our experimental results around the X points, but not around the Γ point, indicating areas of strong renormalization located near Γ. The Ce quasi-particle states participate in the formation of hotspots at the Fermi surface, while the incoherent f states hybridize and lead to the emergence of dispersive features absent in the non-f counterpart BaB 6 . Our results provide a new understanding of the electronic structure in rare-earth hexaborides, which will be useful in elucidating the nature of the exotic low-temperature phases in these materials.