# Perfect Cubes or Cube Numbers

Perfect Cubes or Cube numbers are numbers like 27 that you get if you multiply a whole number by itself three times. For example 27 is that same thing as 3 raised to the third power or (3 * 3 * 3). You can also think of 27 as the volume of a cube whose sides are each 3 units long.

If you list all the cube numbers from 1 to say 8000, you’d have a list like the following:

• 1^3 = 1 * 1 * 1 = 1
• 2^3 = 2 * 2 * 2 = 8
• 3^3 = 3 * 3 * 3 = 9
• and so on …

Take a look at those numbers and you’ll see the following patterns in them:

• The cube of an even number is always an even number.
• The cube of an odd number is always an odd number.

There is also the following relationship between the digit in the 1’s place in any number and the cube of that number:

• If the 1’s place value in the number has a digit 1, the 1’s place value in the cube of that number has a 1 as well.
• If the 1’s place value in the number has a digit 2, the 1’s place value in the cube of that number has an 8.
• 3 then 7
• 4 then 4
• 5 then 5
• 6 then 6
• 7 then 3
• 8 then 2
• 9 then 9
• 0 then 0.

In the list above, the first numbers are the 1’s digit in the number and the second number are the respective 1’s digit in the cube of that number.

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