We report on Raman scattering by electronic intersubband excitations of a modulation-doped GaAs–Al0.2Ga0.8As quantum well embedded inside an AlAs–Al0.4Ga0.6As planar λ microcavity. In optical double-resonance conditions, i.e., when both the exciting laser and the scattered light are in resonance with the cavity, the excitations are experimentally enhanced by a factor of 1500 compared to single-resonant case. In a model calculation, we find a good agreement between theory and experiment.