Perfect Cubes 1 - 1000000

About This Table

The Perfect Cube Tool above the table answers three kinds of questions
"Is N a cube?" tests any number: the tool reports the result and highlights the nearest cubes in the table
"Cube of N" computes N cubed for any integer and jumps to that cell with its details open
"Range" finds and highlights every perfect cube that falls between two numbers you enter
Each table cell shows the cube root and the cube for one of the 100 perfect cubes from 1 to 1,000,000
Cells are color-coded by the root's last digit, revealing the cubing involution: digits 0, 1, 4, 5, 6, 9 are fixed, while 2 swaps with 8 and 3 swaps with 7
Hover any cell to see the gap to the next perfect cube, which is always 3n^2 + 3n + 1
Click a cell to open a details panel with prime factorizations of cube and root, digit sum, last-digit mapping, mod 9 value, and property tags
The Patterns section has five filters: palindromic cubes, cubes that are also squares (sixth powers), cubes with prime roots, cubes of triangular numbers, and cubes preserving the last digit
The Properties section explains four facts: n^3 as a sum of n consecutive odd numbers (with a visual dot pyramid), the last-digit involution, the gap formula 3n^2 + 3n + 1, and the mod 9 rule (cubes are 0, 1, or 8 mod 9)
The built-in quiz at the bottom lets you test your recall, with score persisting for the visit

Additional resources

Root Calculator

Perfect Cube Tool

Every answer takes you to the table. Pick a question:

Last-digit involution

0³ ends in 01³ ends in 12³ ends in 83³ ends in 74³ ends in 45³ ends in 56³ ends in 67³ ends in 38³ ends in 29³ ends in 9

Every digit 0–9 can be the last digit of a cube. The last digit of n³ is fully determined by the last digit of n: it stays the same for 0, 1, 4, 5, 6, 9 and swaps for 2↔8 and 3↔7.

1 — 1,000

∛1 = 1

∛8 = 2

∛27 = 3

∛64 = 4

∛125 = 5

∛216 = 6

∛343 = 7

∛512 = 8

∛729 = 9

∛1,000 = 10

1,331 — 8,000

∛1,331 = 11

∛1,728 = 12

∛2,197 = 13

∛2,744 = 14

∛3,375 = 15

∛4,096 = 16

∛4,913 = 17

∛5,832 = 18

∛6,859 = 19

∛8,000 = 20

9,261 — 27,000

∛9,261 = 21

∛10,648 = 22

∛12,167 = 23

∛13,824 = 24

∛15,625 = 25

∛17,576 = 26

∛19,683 = 27

∛21,952 = 28

∛24,389 = 29

∛27,000 = 30

29,791 — 64,000

∛29,791 = 31

∛32,768 = 32

∛35,937 = 33

∛39,304 = 34

∛42,875 = 35

∛46,656 = 36

∛50,653 = 37

∛54,872 = 38

∛59,319 = 39

∛64,000 = 40

68,921 — 125,000

∛68,921 = 41

∛74,088 = 42

∛79,507 = 43

∛85,184 = 44

∛91,125 = 45

∛97,336 = 46

∛103,823 = 47

∛110,592 = 48

∛117,649 = 49

∛125,000 = 50

132,651 — 216,000

∛132,651 = 51

∛140,608 = 52

∛148,877 = 53

∛157,464 = 54

∛166,375 = 55

∛175,616 = 56

∛185,193 = 57

∛195,112 = 58

∛205,379 = 59

∛216,000 = 60

226,981 — 343,000

∛226,981 = 61

∛238,328 = 62

∛250,047 = 63

∛262,144 = 64

∛274,625 = 65

∛287,496 = 66

∛300,763 = 67

∛314,432 = 68

∛328,509 = 69

∛343,000 = 70

357,911 — 512,000

∛357,911 = 71

∛373,248 = 72

∛389,017 = 73

∛405,224 = 74

∛421,875 = 75

∛438,976 = 76

∛456,533 = 77

∛474,552 = 78

∛493,039 = 79

∛512,000 = 80

531,441 — 729,000

∛531,441 = 81

∛551,368 = 82

∛571,787 = 83

∛592,704 = 84

∛614,125 = 85

∛636,056 = 86

∛658,503 = 87

∛681,472 = 88

∛704,969 = 89

∛729,000 = 90

753,571 — 1,000,000

∛753,571 = 91

∛778,688 = 92

∛804,357 = 93

∛830,584 = 94

∛857,375 = 95

∛884,736 = 96

∛912,673 = 97

∛941,192 = 98

∛970,299 = 99

∛1,000,000 = 100

Patterns to explore

Click a card to highlight every matching cube in the table above.

↔

Palindromic cubes

Cubes that read the same forwards and backwards.

2 in tableClick to highlight

n⁶

Cubes that are also squares

Sixth powers — cubes whose root is itself a perfect square.

10 in tableClick to highlight

Cubes with prime roots

Cubes of prime numbers — their only divisors are 1, p, p², and p³.

25 in tableClick to highlight

△

Cubes of triangular numbers

Cubes whose root is triangular: 1, 3, 6, 10, 15, 21…

13 in tableClick to highlight

Cubes preserving root’s last digit

Cubes whose last digit matches their root — happens for roots ending in 0, 1, 4, 5, 6, 9.

60 in tableClick to highlight

Properties of perfect cubes

Facts true of every perfect cube — useful for spotting them and ruling them out.

Sum of consecutive odd numbers

n³ equals the sum of n consecutive odd numbers. 1³=1; 2³=3+5; 3³=7+9+11; 4³=13+15+17+19.

Last-digit involution

Cubing preserves the last digit for 0, 1, 4, 5, 6, 9 and swaps 2↔ 8 and 3↔ 7. So a cube’s last digit fully determines its root’s last digit.

∛27 ends in 3 → root ends in 3 · ∛512 ends in 2 → root ends in 8

Gap = 3n² + 3n + 1

The difference between n³ and (n+1)³ is always 3n² + 3n + 1.

10³=1000, 11³=1331, gap=331=3(100)+3(10)+1

mod

Mod 9 rule

Every perfect cube is 0, 1, or 8 mod 9 — never 2, 3, 4, 5, 6, or 7. A fast rejection test.

1543 mod 9 = 7 → not a cube