Cube number: Number obtained when a it is multiplied by itself three times.
33 = 3 x 3 x 3 = 27, 43 = 4 x 4 x 4 = 64 etc.
Numbers that can be expressed as sum of two cubes in two different ways are known as Ramanujan numbers. Example, 1729, 4104, 13832 etc.
Numbers obtained when a number is multiplied by itself three times are known as Cube Numbers. For example, 1, 8, 27, ... etc.
If in prime factorization of any number each factor appears three times, then the number is a Perfect Cube.
The symbol denotes cube root. Example, = 4.
Perfect Cube: A natural number is said to be a perfect cube if it is the cube of some natural number. Example: 8 is perfect cube, because there is a natural number 2 such that 3 8 = 2, but 18 is not a perfect cube, because there is no natural number whose cube is 18.
The cube of a negative number is always negative.
Properties of Cube of Number:
Cubes of even number are even.
Cubes of odd numbers are odd.
The sum of the cubes of first n natural numbers is equal to the square of their sum.
Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively.
Cube of the number ending in 2 ends in 8 and cube of the number ending in 8 ends in 2.
Cube of the number ending in 3 ends in 7 and cube of the number ending in 7 ends in 3.