18: CUBE NUMBERS - FACTS

LIST of CUBE NUMBERS:

Cubes of Natural Numbers

NUMBERCUBE
0'00'0
11
28
327
464
5125
6216
7343
8512
9729
101000
111331
121728

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, ...

FEW FACTS ABOUT CUBE NUMBERS

  1. Cubes END in any digit

  2. If Numbers end in 1, 4, 6, 9;
    Cubes also end in 1, 4, 6, 9

  3. No. ends in 2; Cube ends in 8
  4. No. ends in 8; Cube ends in 2

  5. No. ends in 3; Cube ends in 7
  6. No. ends in 7; Cube ends in 3

  7. Cube ends in 0, actually ends in 000

  8. Cube ends in 5,
    actually ends in a multiple of 125

  9. Consec. cubes differ by
    1, 7, 19, 37, 61, 91, 127, 169, ...

  10. NOTE: These 'differences' differ by
    6, 12, 18, 24, 30, ...

  11. Consec. cubes differ by
    1 more than 'a multiple of 6'

  12. Calculating the next cube:
    Increase the smaller cube by
    1 more than
    '3 times the prod. of their bases'


  13. For example:
    3 3 = 2 3 + [3(2 x 3) + 1] [or]
    31 3 = 30 3 + [3(30 x 31) + 1]
    31 3 = 27000 + 2791 = 29791