Cube and Cube Roots in Mathematics

Updated on October 26, 2025 | By Learnzy Academy

When a number is multiplied by itself three times, the result is called its cube. 
The cube of a positive number is positive, and the cube of a negative number is negative. 
A number is called a perfect cube if it is the cube of a whole number, such as 1, 8, 27, 64, 125, etc. 
The cube root of a number is the number whose cube gives the original number. For example, the cube root of 27 is 3. 
Cube roots can be found by the prime factorisation method or estimation. 
Cubes and cube roots are used in finding the volume and side of cubes in geometry. 
Some important cube identities are (a + b)³ = a³ + b³ + 3ab(a + b) and (a – b)³ = a³ – b³ – 3ab(a – b).

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List of question on "Cube and Cube Roots"

  1. The sum of the cubes of two numbers is 189. If one number is twice the other, find both numbers.
  2. The cube root of a number is 12. What will be the cube root of its 1/27th part?
  3. A cube-shaped ice block of side 10 cm is cut into 1000 smaller cubes of equal size. Find the side of each small cube.
  4. A metal cube of side 6 cm is melted and recast into smaller cubes of side 2 cm. How many small cubes are formed?
  5. Without finding the cube, find the unit digit of 93³ + 47³.
  6. A cube’s volume increases from 27 cm³ to 64 cm³. Find the percentage increase in its edge.
  7. If a³ = 729, find the value of a².
  8. Find the cube root of 64 × 125 × 8 × 27
  9. Find the cube root of the product of 64 and 125.
  10. A cube has a surface area of 150 cm². Find its side length (approximate).
  11. Find the cube of 0.3
  12. Find the cube root of 125 × 64
  13. Find the smallest number by which 392 must be divided to get a perfect cube.
  14. Find the smallest number by which 648 must be multiplied to make it a perfect cube.
  15. A number multiplied by itself three times gives 729. Find the number.
  16. Find the cube root of 17576 by the prime factorisation method.
  17. If the cube of a number ends in 1, what will be the unit digit of the number?
  18. The cube root of a number is 9. Find the number.
  19. The side of a cube is doubled. How many times will its volume increase?
  20. A cube has a volume of 512 m³. Find its surface area.
  21. A metal cube of side 5 cm is melted to form small cubes each of side 1 cm. How many small cubes are formed?
  22. The volume of a cube is 1331 cm³. Find the length of its edge.