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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
p

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.

Σ

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.

135791113151719
d

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
Δ

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
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