Based on first-principles calculations, we show that very high-density periodic arrays of Nb4 clusters with both the tetrahedron and quadrangle configurations can be stably absorbed on the Cu(111) and Cu(100) surfaces,with the quadrangle configurations more stable than the tetrahedron ones. The strong covalent bonding between atoms within the Nb4 clusters contributes to the stability of Nb4 adsorptions on the Cu surfaces.