A figurate number which is constructed as a centered cube with a square pyramid appended to each face,
(1)
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(2)
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where is a centered cube number and is a square pyramidal number. The first few are 1, 15, 65, 175, 369, 671, ... (OEIS A005917). The generating function of the rhombic dodecahedral numbers is
(3)
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A related set of numbers is the number of cubes in the Haűy construction of the rhombic dodecahedron, given by
(4)
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for an odd number. Re-indexing with then gives
(5)
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giving the first few values 1, 33, 185, 553, 1233, ... (OEIS A046142).