Prove that if a number is doubled, then its cube is eight times the cube of the given number.

Prove that if a number is tripled then its cube is 27 times the cube of the given number.

Find the cube of rational number 3.1.

The average of thrice the cube of a number and twice the square of the same number equals eight times the same number . Given that the number is a positive integer, what is the number?

If the length of a side of a cube is doubled, then the ratio of the volume of new cube and original cube is

Show that 0.001728 is the cube of a rational number.

The sum of two numbers is 7 and the sum of their cubes is 133. Find the sum of their squares

Find all 3-digit numbers which are the sums of the cubes of their digits.

If the sum of two numbers is 5 and the sum of their cubes is 35, find the sum of their squares

State true or false. (i) Cube of any odd number is even. (ii) A perfect cube does not end with two zeros. (iii) If square of a number ends with 5, then its cube ends with 25. (iv) There is no perfect cube which ends with 8. (v) The cube of a two digit number may be a three digit number. (vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number.

Divide the number 26244 by the smallest number so that the quotient is a perfect cube. Also fine the cube root of the quotient.