Square and Cube Numbers for Kids: What They Are and How to Learn Them

By the Success Tutoring team · 5 October 2026

A square number is what you get when you multiply a number by itself, such as 4 × 4 = 16. A cube number is a number multiplied by itself three times, such as 2 × 2 × 2 = 8. The names come from shapes: square numbers of dots make squares, and cube numbers of blocks make cubes. Building them with real objects is the best way to start.

Step 1: Build square numbers

Give your child some counters or coins and ask them to make squares: 1 by 1, 2 by 2, 3 by 3 and so on. Count how many counters each square needs: 1, 4, 9, 16, 25. These are the square numbers.

We write 4 × 4 as 4² and say “four squared”. The small 2 means “multiply two of these together”.

Step 2: Build cube numbers

Use building bricks, sugar cubes or dice. A 2 by 2 by 2 cube needs 8 small cubes, and a 3 by 3 by 3 cube needs 27. We write 3 × 3 × 3 as 3³ and say “three cubed”.

Square and cube numbers to learn

Most children are expected to know the squares up to 12² and the cubes up to 5³ (plus 10³ = 1,000). The squares are already hiding in the times tables: they run diagonally across a multiplication grid. A few minutes with the Times Tables Challenge keeps them fresh.

Square roots and cube roots

A square root goes backwards: it asks “what number squared makes this?” The square root of 49, written √49, is 7 because 7² = 49. A cube root works the same way for cubes: the cube root of 27 is 3.

Children can also estimate: √50 must be just over 7, because 7² = 49 and 8² = 64.

Patterns children love

• The gaps are odd numbers. 1, 4, 9, 16, 25: the differences are 3, 5, 7, 9. Each square is built by adding the next odd number, which you can see by adding an L-shaped border to your counter square.
• Odd numbers add up to squares. 1 + 3 + 5 + 7 = 16, which is 4².
• Square numbers have an odd number of factors. 16 has the factors 1, 2, 4, 8 and 16, because 4 pairs with itself. Every other kind of number has an even number of factors.
• Square numbers only end in 0, 1, 4, 5, 6 or 9. So 47 and 83 can't be square numbers.
• Some numbers are both. 1 and 64 are square numbers and cube numbers (64 = 8² = 4³). The next one is 729 (27² and 9³).

A quick trick: squaring numbers that end in 5

To square a number ending in 5, multiply the tens digit by the next number up, then write 25 on the end:

• 35²: 3 × 4 = 12, so 1,225.
• 45²: 4 × 5 = 20, so 2,025.
• 65²: 6 × 7 = 42, so 4,225.

Where square and cube numbers are used

• Area: a square with sides of 7 cm has an area of 7² = 49 cm².
• Volume: a cube with edges of 4 cm has a volume of 4³ = 64 cm³.
• Order of operations: in 2 × 5², the square comes first, so it's 2 × 25 = 50. See our guide to the order of operations.
• Famous patterns: 3² + 4² = 9 + 16 = 25 = 5², which is the start of Pythagoras' theorem in secondary school.

Common mistakes

• Multiplying by 2 instead of squaring. 5² is 5 × 5 = 25, not 5 × 2 = 10.
• Multiplying by 3 instead of cubing. 3³ is 3 × 3 × 3 = 27, not 9.
• Mixing up squares and square roots. 9² = 81, but √9 = 3.
• Thinking every big round number is a cube. 100 isn't a cube number: 4³ = 64 and 5³ = 125, so it falls in between.

When do children learn square and cube numbers?

Children usually meet square numbers through arrays and times tables earlier on, then learn the names, the notation and cube numbers around Grade 5 to Grade 6. Square numbers link closely to factors, so our guide to prime numbers and factors is a natural next read.

Frequently asked questions