Sum of digits of a Cube

The sum of any cube when reduced to a single digit will always be either 1, 8, or 9.

For Example:

5³ = 125 = 1+2+5 =8
9³ = 729 = 7+2+9 = 18=1+8=9
17³ = 4913=4+9+1+3=17=1+7=8
4³=64=6+4=10=1+0=1

Also, they follow a cycle. The numbers 1 ,8, and 9 appear in order:

1 - sum of the digits of cube of 1 would be 1
2 - would be 8
3 - would be 9
4 - would be 1 (4³ = 64 = 6+4 = 10= 1+0 = 1)
5 - would be 8 (5³ = 125 = 1+2+5 = 8)
6 - would be 9 (6³ = 216 = 2+1+6 = 9)

so on and so forth.