Efficient excitation of Fano resonances in plasmonic systems usually requires complex nano-structure geometries and some degree of symmetry breaking. However, a single-layered concentric core-shell particle presents inherent Fano profiles in the scattering spectra when sphere and cavity modes spectrally overlap. Weak hybridization and suitable choice of core and shell materials gives rise to strong electric dipolar Fano resonances in these systems and retardation effects can result in resonances of higher multipolar order or of magnetic type. Furthermore, suitable tailoring of illumination conditions leads to an enhancement of the Fano resonance by quenching of unwanted electromagnetic modes. Overall, it is shown that single layered core-shell particles can act as robust Fano resonators.