## Cube (algebra) - Wikipedia, the free encyclopedia

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** Cube (algebra) **

"Third power" redirects here. For the band, see Third Power.
"Cubed" redirects here. For other uses, see Cube (disambiguation).
"Â³" redirects here. Its literal meaning is the numeral "3" in
superscript.
/y/ = /x/^3 for values of 0 â¤ /x/ â¤ 25.

In arithmetic and algebra, the *cube* of a number n is its third power: the
result of the number multiplied by itself twice:

/n/^3 = /n/ Ã /n/ Ã /n/.

It is also the number multiplied by its square:

/n/^3 = /n/ Ã /n/^2.

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

Both cube and cube root are odd functions:

(â/n/)^3 = â(/n/^3).

The cube of a number or any other mathematical expression is denoted by a
superscript 3, for example 2^3 = 8 or (/x/ + 1)^3.

*Contents*

· 1 In integers

· 1.1 Base ten
· 1.2 Waring's problem for cubes
· 1.3 Fermat's last theorem for cubes
· 1.4 Sum of first /n/ cubes
· 1.5 Sum of cubes of numbers in arithmetic progression
· 1.6 Cubes as sums of successive odd integers

· 2 In rational numbers
· 3 In real numbers, other fields, and rings
· 4 History