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Strong coupling between cavity photons and molecular vibrations can lead to the formation of vibron-polaritons. In a recent experiment with PVAc molecules in a metal-metal microcavity [A.Shalabney et al., Ang.Chem.Int.Ed. 54 7971 (2015)], such a coupling was observed to enhance the Raman scattering probability by several orders of magnitude. Inspired by this, we theoretically analyze the effect of strong photon-vibron coupling on the Raman scattering amplitude of organic molecules. This problem has recently been addressed in [J.del Pino, J.Feist and F.J.Garcia-Vidal; J.Phys.Chem.C 119 29132 (2015)] using exact numerics for a small number of molecules. In this paper we derive compact analytic results for any number of molecules, also including the ultra-strong coupling regime. Our calculations predict a division of the Raman signal into upper and lower polariton modes,with some enhancement to the lower polariton Raman amplitude due to the mode softening under strong coupling., Comment: 11 pages, 4 figures