The lyotropic cubic phase of space group Fd3m has been observed for the first time in a purely binary amphiphile/water system, consisting of fully-hydrated synthetic 1,2-di-O-alkyl-3-O-(alpha-or beta-D-xylopyranosyl)-sn-glycerols. These glycolipids are saturated analogues of naturally-occurring membrane lipids, with the polar headgroup chemically modified to render it less hydrophilic. A number of chain lengths of these alpha- and beta-anomers in the range from C12 to C19 have been studied, and we find that the Fd3m cubic phase is suppressed when the chain length is reduced to C14 or shorter. The relative intensities of the X-ray Bragg peaks are similar to those of previously observed Fd3m phases, which have been shown to have an inverse micellar structure, implying that the glycolipid Fd3m cubic phase described here also consists of the same complex packing of inverse Micelles.