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