Depending on whether a number is odd or even, its cube number is also odd or even respectively.

This is determined by the nature of the cube numbers’ unit digit.

- If a number is odd, its cube numbers’ unit digit is also odd.
- If a number is even, its cube numbers’ unit digit is also even.

The table below shows the units digit of a number and the units digit of the cube of that number:

Units digit of number | Units digit of its cube |

1 | 1 |

2 | 8 |

3 | 7 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 3 |

8 | 2 |

9 | 9 |

In the **prime factorisation** of any number, if** each prime factor** appears **three times**, then the number is a **perfect cube**.

Consider, the number . By prime factorisation,

Hence, is a perfect cube.

Consider, the number . By prime factorisation,

In the above prime factorisation 2 appears twice.

Hence, is not a perfect cube.

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