Properties of Cube

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Some properties of cubes of natural numbers are:-

Property 1: Cubes of all even numbers are even.
Example: 6³ = 6 x 6 x 6 = 216
6 and 216 both are even numbers.

Property 2: Cubes of all odd natural numbers are odd.
Example: 7³ = 7 x 7 x 7 = 343
7 and 343 both are natural odd numbers.

Property 3: The sum of the cubes of first n natural numbers is equal to the square of their sum.
1³ + 2 ³ + 3³ + … + n³ = (1 + 2 + 3 + … + n)²
Example: 1³ + 2³ + 3³ + 4³ = (1 + 2 + 3 + 4)³
1 + 8 + 27 + 64 = (10)²
100 = 100

Property 4 : Cubes of the numbers ending in digit 1, 4, 5, 6 and 9 are the numbers ending in the same digit.

Numbers	Cubes
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000

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Practice
1) Express 8³ as sum of odd natural numbers.
2) Find the odd numbers to be added to get the following cubes.
a) 7³.
b) 12³
c) 4³

3) State the unit digits of the cubes of the following numbers.
a) (387)³
b) (83)³
c) (-81)³
d) (55)³
e) (680)³

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Cube and Cube Roots

• Cube of Numbers
• Perfect Cube
• Properties of Cube
• Cube by Column method
• Cube of Negative numbers
• Cube of Rational numbers
• Cube-Root
• Finding cube-root by Prime Factorization
• Cube root of Rational numbers
• Estimating cube root

From Properties of cube to Exponents

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