Perfect Cubes Calculator
Check whether a number is a perfect cube, explore the table of cubes 1³–100³, and find the nearest perfect cube above or below any value — with exact integer math.
Perfect cube checker
Enter any whole number (negatives and 0 allowed). We take the integer cube root and verify k³ exactly — never a float guess. Try 1728 (= 12³) or 100 (not a perfect cube). Landmarks: 20³ = 8000, 50³ = 125000, 100³ = 1000000.
Table of perfect cubes 1³–100³
Every perfect cube from 1 to 1,000,000 (100³), plus the gap to the previous cube. It starts 1,8,27,64,125,216,343,512,729,1000 and keeps going to 1000000. Spot the pattern: the gap grows as 3k²+3k+1 — e.g. 10³ − 9³ = 1000 − 729 = 271.
| k | k³ | gap from (k−1)³ |
|---|
Nearest perfect cube
For any whole number, find the closest perfect cube below and above it. Example: below 100 the nearest cube is 64 (4³); above 100 it is 125 (5³) — and 125 is closer (25 away) than 64 (36 away).
Last-digit pattern of perfect cubes
Every last digit 0–9 is possible. The last digit of n³ depends only on the last digit of n:
| n ends in | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| n³ ends in | 0 | 1 | 8 | 7 | 4 | 5 | 6 | 3 | 2 | 9 |
Frequently asked questions
What is a perfect cube?
A perfect cube is a whole number that can be written as k^3 for some integer k. The first ten perfect cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 (that is, 1^3 through 10^3).
How do you check if a number is a perfect cube?
Take the integer cube root of n (round n^(1/3) to the nearest whole number k), then verify that k^3 equals n exactly - never trust the floating-point approximation alone. For example, 1728 is a perfect cube because 12^3 = 1728, while 100 is not a perfect cube (it sits between 4^3 = 64 and 5^3 = 125). This calculator uses exact integer arithmetic, so even huge inputs like 1000000 = 100^3 are decided correctly.
What is the nearest perfect cube to 100?
Below 100, the nearest perfect cube is 64 (4^3); above 100, it is 125 (5^3). The cube above is actually closer: 125 is 25 away, while 64 is 36 away.
What is the pattern between consecutive perfect cubes?
The gap between (k+1)^3 and k^3 follows the formula 3k^2 + 3k + 1, so gaps keep growing. Example: 10^3 - 9^3 = 1000 - 729 = 271, and 3(9)^2 + 3(9) + 1 = 243 + 27 + 1 = 271. Further out, 100^3 - 99^3 = 1000000 - 970299 = 29701.
Can a perfect cube end in any digit?
Yes - every digit 0-9 is possible. The last digit of n^3 depends only on the last digit of n: 0->0, 1->1, 2->8, 3->7, 4->4, 5->5, 6->6, 7->3, 8->2, 9->9. Unlike perfect squares (which can never end in 2, 3, 7 or 8), perfect cubes have no forbidden last digit.
Can negative numbers be perfect cubes?
Yes. A negative number is a perfect cube when its absolute value is one: for example, -27 = (-3)^3, and 0 = 0^3 is also a perfect cube. This checker handles negatives and zero exactly.
What is the difference between this and an nth root calculator?
This is a perfect-cube specialist: it checks whether numbers are perfect cubes, lists the cubes 1^3 to 100^3 (up to 1000000), shows gap and digit patterns, and finds the nearest cube above or below any value. For the cube root (or any root) of numbers that are NOT perfect cubes - like the cube root of 50 - use a general nth root calculator instead.
Free tool by NRTechStudio