We study the extended Jaynes-Cummings-Hubbard model on the triangular and one-dimensional cavity lattices. By using mean-field and density matrix renormalization group methods, we observe various types of solids with different density patterns and find evidences for light supersolids. The triangular lattices exhibit extended supersolid regions in the phase diagram. Apart from the holeexcited supersolid phase, we also see an additional supersolid phase. Besides, novel pair correlations are found due to the interplay between the atoms in the cavities and atom-photon interaction. On the one-dimensional lattices both for the hardcore and softcore models, we find indications for a particle-excited or a hole-excited supersolid phase emerging around the solid phase. Beats emerge within the SS phase for the density-density correlation in both hardcore and softcore models. The results are helpful in guiding experimentalists in realizing novel quantum phases on optical lattices.