Two single crystals of fully dehydrated $Rb^+$ -exchanged zeolite A have been prepared by the reduction of all $Ca^{2+}$ ions in dehydrated $Ca_6$-A by rubidium vapor. Their structures were determined by single crystal X-ray diffraction methods in the cubic space group Pm3m (a=12.160(2) $^{AA}$ and 12.166(2) $^{AA}$) at 22(1)$^{circ}$C. In these structures, 12.4(2) to 13.3(2) Rb species are found per unit cell, more than 12 Rb$^+$ ions needed to balance the anionic charge of the zeolite framework, indicating that the sorption $Rb^0$ has occurred. In each structure, three $Rb^+$ ions per unit cell are located at the centers of the 8-rings. Six to eight $Rb^+$ ions are found opposite the 6-rings on threefold axes, and three $Rb^+$ ions are found in a sodalite unit. About 0.5 $Rb^+$ ion lies opposite a 4-ring. The structural analysis indicates the presence of a triangular rubidium cluster in the sodalite cavities. The triangular rubidium clusters may be stabilized by the coordination to two and/or three rubidium ions in the large cavity. Therefore, this cluster may be viewed as $(Rb_5)^{4+}$ and/or $(Rb_6)^{4+}$.