18: CUBE NUMBERS - FACTS

__LIST of CUBE NUMBERS:__

__Cubes of Natural Numbers__
NUMBER | CUBE |

0 | '00'0 |

1 | 1 |

2 | 8 |

3 | 27 |

4 | 64 |

5 | 125 |

6 | 216 |

7 | 343 |

8 | 512 |

9 | 729 |

10 | 1000 |

11 | 1331 |

12 | 1728 |

0, 1, 8, 27, 64, 125, 216, 343, 512,

**729**, 1000, 1331, 1728, 2197, 2744, 3375, ...

#### FEW FACTS ABOUT CUBE NUMBERS

- Cubes END in any digit

- If Numbers end in 1, 4, 6, 9;

Cubes also end in 1, 4, 6, 9

- No. ends in 2; Cube ends in 8
- No. ends in 8; Cube ends in 2

- No. ends in
**3**; Cube ends in **7**
- No. ends in
**7**; Cube ends in **3**

- Cube ends in 0, actually ends in
**000**

- Cube ends in 5,

actually ends in a multiple of **125**

- Consec. cubes differ by

1, 7, 19, 37, 61, 91, 127, 169, ...

__NOTE:__ These 'differences' differ by

6, 12, 18, 24, 30, ...

- Consec. cubes differ by

1 more than 'a multiple of 6'

__Calculating the next cube:__

Increase the smaller cube by

**1 more than**

'3 times the prod. of their bases'

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