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 :-
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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