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Encyclopedia > Cube (arithmetic)

In arithmetic and algebra, the cube of a number n is its third power — the result of multiplying it by itself two times:

n3 = nnn.

This is also the volume formula for a geometric cube of side length n, giving rise to the name.

The term cube or cube number is often used to refer to a perfect cube i.e. a number that is the cube of a positive integer.

The series of perfect cubes starts as follows:

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, ...

The inverse operation of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power.

Every positive integer can be written as the sum of nine cubes or fewer; see Waring's problem. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be written as the sum of fewer than nine cubes :-

23 = 23 + 23 + 13 + 13 + 13 + 13 + 13 + 13 + 13

Each cube number n3 is also the sum of the first n centered hexagonal numbers, although representing a different shape. Results from FactBites:

 CUBE - OneLook Dictionary Search (410 words) cube, cube : Encarta® World English Dictionary, North American Edition [home, info] Cube, cube : UltraLingua English Dictionary [home, info] cube, cube (m) : AllWords.com Multi-Lingual Dictionary [home, info]
 Cube - Wikipedia (251 words) The cube is a special kind of square prism and of triangular trapezohedron[?], and is dual to the octahedron. A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular compound of five cubes. In arithmetics and algebra, the cube of an entity x is the result of multiplying it with itself two times.
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