Cube a number and you get the volume of a real box of blocks. The cube root just reads the side length back.
Start hereWhen you cube a number, you multiply it by itself three times — and the answer is exactly how many little blocks it takes to build a solid cube that many blocks wide.
We write it with a tiny 3 floating up high: 2³ = 2 × 2 × 2 = 8. That little 3 is called the index (some people say exponent) — it counts how many times the number gets multiplied. A number you can build into a perfect cube like this is called a cube number.
Picture a single tiny block — a cube one unit on every side. Now imagine building a bigger cube out of those tiny blocks. To make it, you have to go three ways at once: across, back, and up.
If your cube is 2 blocks wide, it's also 2 blocks deep and 2 blocks tall. So the number of blocks is 2 (across) × 2 (deep) × 2 (up) = 8. That "three ways at once" is the whole reason we multiply three times — one multiply for each direction of space. A flat square only needs two directions, so you'd only multiply twice (that's 2² = 4, a square number). A cube lives in 3D, so it gets a third multiply.
Quick vocab: the small raised number is the index or exponent. An index of 2 means "square it," and an index of 3 means "cube it." From here on, cubing always means: use the number three times and multiply.
Drag the slider to choose how wide the cube is. Watch it stack up in 3D, and read the block count — that number is the cube.
A single block. One cube, one unit wide — the smallest cube number there is.
Notice the pattern as you drag: every time you add one to the side length, the block count jumps by a lot. Going from 2 to 3 doesn't add 1 block — it leaps from 8 blocks to 27. That's because you're adding a whole new slab across, back, and up all at once. Cube numbers grow fast.
Here's the same move done by hand. Slide the demo above to each of these to watch the stack match the maths:
2 × 2 × 2. A cube 2 blocks wide takes 8 little blocks.
3 × 3 × 3. Three blocks in every direction: 27 in all.
4 × 4 × 4. Already 64 blocks — see how quickly it climbs?
A safe way to do it in your head: cube 4 by first squaring — 4 × 4 = 16 — then multiply by 4 one more time: 16 × 4 = 64. Square first, then take one more step up into the third direction. That trick works for any number.
Cubing goes side length → number of blocks. The cube root goes the other way: you're handed a pile of blocks that forms a perfect cube, and you answer how wide is one side?
We write it with a little tick and a tiny 3: ∛27 = 3, read as "the cube root of 27 is 3." It's asking, what number, cubed, gives 27? Since 3³ = 27, the answer is 3. Cubing and cube-rooting are a matched pair — each one undoes the other, like tying and untying a shoelace.
Tap a cube number below. The blocks rebuild themselves, and the side length — the cube root — is measured out along the front edge for you.
∛1 = 1. A single block is 1 wide — the tiniest cube of all.
Every number on those buttons is a genuine cube number, so its cube root is a tidy whole number. Most numbers aren't perfect cubes — you can't stack 10 blocks into a solid cube without leftovers — so their cube roots are messy decimals. But the idea never changes: a cube root is always just the length of one side of the cube.
Cube numbers aren't just a classroom trick — they measure volume, the amount of space inside something box-shaped:
The little "³" in cm³ is the very same index 3 you've been using. Volume is measured in cubes, so its unit is literally a cubed length.
Three quick questions. Pick an answer and it'll tell you right away.
Use the number three times and multiply: 4³ = 4 × 4 × 4 = 64. One multiply for each direction of a 3D cube.
The answer counts the unit blocks in a solid cube n wide — the space it fills. That's why volume uses ³.
The cube root reads the side length back: ∛27 = 3, because 3³ = 27. Tie the lace, untie the lace.