We present a method for efficiently generating Poisson sphere distributions, the three-dimensional equivalent of Poisson disk distributions. Our method is able to generate arbitrarily large Poisson sphere distributions in real time, and allows local evaluation of the generated distributions. The method we present is based on cubes with colored corners, called corner cubes, an extension of corner tiles. We generalize tiling algorithms and construction methods from corner tiles to corner cubes. Poisson sphere distributions have several useful applications in computer graphics, such as geometry instancing and a three-dimensional procedural object distribution function.