Doping of silicon clusters with transition metals can enhance the stability of such clusters and confer many peculiar physical and chemical properties. Therefore, this method occupies an important position in the fields of new energy and materials science. Herein, we report the geometric structures as well as electronic and thermodynamic properties of CoSi₁₆^- and Co₂Si₃₂^2- clusters using the particle swarm optimization algorithm CALYPSO searching method and density functional theory. Results indicate that the lowest structures of the CoSi₁₆^- and Co₂Si₃₂^2- clusters exhibit the highly symmetric D_2d and D_2h point structures, respectively, in which the Co atom is completely encapsulated in Si cages. Based on these structures, various electronic properties, including the magnetic properties and bond order, are systemically evaluated. In addition, the photoelectron spectra, infrared spectra, and Raman spectra are recorded to identify the main characteristic peaks of the two systems. Finally, the thermodynamic properties of the two systems are investigated. Moreover, the temperature dependence of C_v and S for the CoSi₁₆^- and Co₂Si₃₂^2- clusters is discussed.