The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically within a microscopic realistic model of dielectrics for an arbitrary physically possible frequency dispersion of dielectric permittivity ε(iω). Divergences are absent in calculations, a minimum interatomic distance λ is a physical cut-off. Casimir surface force is proved to be attractive. A physical definition of the Casimir energy is discussed.