Large octahedral and cuboctahedral palladium clusters, ranging from Pd-55 to Pd-146, have been investigated by means of all-electron relativistic density functional calculations. Adsorption of CO molecules on the (111) facets of these clusters was also studied. In particular, we focused on the interaction of CO (a single molecule per facet) with threefold hollow sites to inspect the variation of the calculated adsorption parameters with cluster size. We considered how observables calculated for that adsorption position on cluster facets relate to adsorption properties of the corresponding site at the single crystal surface Pd(111). We demonstrated for the first time that, with three-dimensional cluster models proposed here, one can reach cluster size convergence even for such a sensitive observable as the adsorption energy on a metal surface. We also addressed size effects on interatomic distances and the cohesive energy of bare Pd nanoclusters whose structure was fully optimized under the imposed O-h symmetry constraint. These quantities were found to correlate linearly with the average coordination number and the inverse of the cluster radius, respectively, allowing a rather accurate extrapolation to the corresponding values of Pd bulk. Finally, we considered the size convergence of adsorption properties of the optimized Pd clusters, as probed by CO adsorption. We also outlined implications of using these symmetric clusters for investigating adsorption and reactions on oxide-supported nanoparticles of model Pd catalysts.