A centered cube number counts a central point surrounded by cubic shells, and equals the sum of two consecutive cubes: \(k^3 + (k+1)^3\). So 9 = 1³ + 2³, 35 = 2³ + 3³, 91 = 3³ + 4³. The sequence: 1, 9, 35, 91, 189, 341, 559, 855.
They're the three-dimensional centered analogue of the [[centered-square]] and [[centered-hexagonal]] numbers. Because each is a sum of consecutive cubes, the centered cube numbers connect neatly to the identity that the sum of the first \(n\) cubes is a perfect square.