The authors consider four-dimensional electrostatics. In 4D the electrostatic multipole moment of order l (l=0, 1/2, 1...) is a tensor with (2l+1)2 independent components. They derive the multipole expansions for the potential due to an arbitrary distribution of charge, and for the energy of a charge distribution in a spatially non-uniform external electric field. They also derive the multipole expansion for the interaction energy of two rigid, non-overlapping charge distributions. The results are expressed in both Cartesian tensor and hyperspherical tensor forms. The transformation properties of the moments, under the symmetry operations of the 4D rotation-reflection group O4, and under translation of the coordinate axis system, are also derived.