Molecular dynamics simulations have been employed to study the thermal response of an Au hollow cube with a side about 8 nm long and walls about 3 run thick. The gradual temperature rise determines the occurrence of a hierarchical sequence of melting transitions regarding atoms with a progressively increasing number of nearest neighbors. Atoms located at the cube edges are thus seen to undergo melting first, then followed by surface and grain boundary species, and finally by atoms in bulklike regions of cube walls. A percolating liquidlike framework connecting external and internal surfaces is formed in the temperature range within which grain boundaries are partially molten. Such framework represents a preferential diffusion path for liquidlike species.