The polarizability of an array of metallic spheres embedded in a dielectric host sphere is obtained by means of a quasi-static analysis of the electromagnetic interaction. The proposed model is validated through comparisons with the results obtained with software based on the finite element method. A parametric study of the polarizability as a function of the number of inclusions, their radii, and their positions is presented. An analysis of the plasmon resonances of the particle as a function of the same parameters is performed.