How to cube two-digit numbers in your head
Cubes get hard fast — but the same "split it up and expand" approach that works for squares works here too, just with one more term to track.
Step one: memorize 1³ through 10³
Do this before anything else — it's the foundation everything else builds on.
1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 6³=216, 7³=343, 8³=512, 9³=729, 10³=1000
The rule for larger numbers
Split the number into tens (a) and units (b), then expand:
It looks like more work than the squares version, and it is — but every one of those four terms only involves numbers you already know from the memorized list above.
Worked example: 12³
Split as a = 10, b = 2.
a³ = 1000
3a²b = 3 × 100 × 2 = 600
3ab² = 3 × 10 × 4 = 120
b³ = 8
Add them: 1000 + 600 + 120 + 8 = 1728.
Worked example: 13³
Split as a = 10, b = 3.
a³ = 1000
3a²b = 3 × 100 × 3 = 900
3ab² = 3 × 10 × 9 = 270
b³ = 27
Add them: 1000 + 900 + 270 + 27 = 2197.
A shortcut inside the shortcut
Always splitting at the tens digit (a = 10, 20, 30...) keeps a³ and the 3a²b term as round, easy multiplications — that's why this method is worth using specifically for two-digit numbers, where a is always a clean multiple of ten.