Cube point picking is the three-dimensional case of hypercube point picking.
The average distance from a point picked at random inside a unit cube to the center is given by
 |  |  | (1) |
 |  |  | (2) |
 |  |  | (3) |
 |  |  | (4) |
Similarly, the average distance from a point picked at random to a fixed corner is given by
 |  |  | (5) |
 |  |  | (6) |
 |  |  | (7) |
 |  |  | (8) |
 |  |  | (9) |
where 
is the 
-box integral.
The average distance from the center of a unit cube to a given face is
 |  |  | (10) |
 |  |  | (11) |
 |  |  | (12) |
 |  |  | (13) |
(OEIS A097047).
