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In this work, we investigate the aspects of photon emitted from a single quantum dot exciton, strongly coupled to a planar nanocavity, from which the exact spectrum is derived. By using the rigorous medium-dependent theory of fully quantized cavity-QED formulas, the exact spectrum is reduced to two separate forms, in terms of the leaky cavity mode emission and the radiation mode emission. In the strong coupling regime, it is concluded that several new effects should be associated with the leaky cavity mode emission, including the appearance of an off-resonance cavity mode and a loss-induced on-resonance spectral triplet. The cavity mode emission is shown to completely dominate the emitted spectrum, even for large cavity-exciton detunings, whereby the usual cavity-QED formulas developed for radiation-mode emission drastically fail. These predictions are in qualitative agreement with several observations reported in recent experiments, and apply to a wide range of semiconductor nanocavity photonic devices.