As the counterpart of electric and magnetic dipoles, the toroidal dipole is of paramount importance in the flourishing fields of metamaterials and Nanophotonics, and has therefore been getting much attention recently. Here, we demonstrate that a toroidal dipole can be formed in (dielectric core)@(plasmonic shell) nanostructures as the core refractive index is increased. For nanostructures with relatively large core refractive indices, polarized charge oscillation can be induced in the core by the oscillation of free electrons in the shell. These two oscillations create a toroidal dipole in the nanostructure. The formation of a toroidal dipole induces a scattering dip and a new absorption peak spectrally close to the created scattering dip. We also show that the toroidal dipole-induced absorption and scattering dip become weaker as the imaginary part of the core refractive index is increased. To the best of our knowledge, this is the first observation that the absorption becomes weaker with the increase of the imaginary part of the refractive index. Moreover, because almost all of the electric and magnetic fields are concentrated within the nanostructure, the toroidal dipole-induced scattering dip and absorption peak show resonance wavelength that is independent of the refractive index of the surrounding medium. Such an invariable property can be used as optical references or marks.