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We demonstrate cavity cooling of all motional degrees of freedom of an atomic ensemble using light that is far detuned from the atomic transitions by several gigahertz. The cooling is achieved by cavity-induced frequency-dependent asymmetric enhancement of the atomic emission spectrum, thereby extracting thermal kinetic energy from the atomic system. Within 100 ms, the atomic temperature is reduced from 200 to , where the final temperature is mainly limited by the linewidth of the cavity. In principle, the technique can be applied to molecules and atoms with complex internal energy structure.