Answer
.366 mgs
Work Step by Step
We will use the terms of the back of the book's solution, which calls the height s. We know that the mass is given the variable m. Using our knowledge of the geometry of cubes, we know that the height of the center of mass (which in this case is the center of the cube) will be .866s above the ground. Thus, it follows:
$\Delta U = .866mgs - .5mgs = .366 mgs$
