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Volume plasmons are collective eigenmodes of the free-electron gas inside a metal. Because of their longitudinal character and the transversal nature of light, the photoexcitation of volume plasmons is forbidden in classical electrodynamics. Nevertheless, we show their existence for metallic nanoshells using analytical solutions of the classical scattering problem. Solely for the case of a vanishing real part of the shell permittivity, a local maximum at the natural plasma frequency appears in the extinction spectra. For explaining our observations, we suggest a simple physical picture which is supported by examples on silver and gold shells.