find the number of possible outcomes for a number cube rolled three times

If a dice is rolled once we get 6 possible outcomes.

If it is rolled 3 times there are 6^3 = 216 possible out comes.

The lowest  number is that we can obtain is 1+1+1 = 3 one way.

The highest number we can get is  6+6+6 = 18.

The possible cube number integer between 1 and 18  is  8.

We can get yhis cube number 8  in the following way.

1+1+6

1+2+5

1+3+4

1+4+3

1+5+2

1+5+1

2+1+5

2+2+4

2+3+3

2+4+2

2+5+1

3+1+4

3+2+3

3+3+2

3+4+1

4+1+3

4+2+2

4+3+1

5+1+2

5+2+1

6+1+1

So there are 21 ways we can obtain acube number 8.