Editing Cube (section)

=== Relation to the spheres ===
With edge length <math> a </math>, the [[inscribed sphere]] of a cube is the sphere tangent to the faces of a cube at their centroids, with radius <math display="inline"> \frac{1}{2}a </math>. The [[midsphere]] of a cube is the sphere tangent to the edges of a cube, with radius <math display="inline"> \frac{\sqrt{2}}{2}a </math>. The [[circumscribed sphere]] of a cube is the sphere tangent to the vertices of a cube, with radius <math display="inline"> \frac{\sqrt{3}}{2}a </math>.{{r|radii}}

For a cube whose circumscribed sphere has radius <math> R </math>, and for a given point in its three-dimensional space with distances <math> d_i </math> from the cube's eight vertices, it is:{{r|poo-sung}}
<math display="block"> \frac{1}{8}\sum_{i=1}^8 d_i^4 + \frac{16R^4}{9} = \left(\frac{1}{8}\sum_{i=1}^8 d_i^2 + \frac{2R^2}{3}\right)^2. </math>