use euclid's division lemma to show that the cube of any positive intiger is of the for 9m,9m+1 or9m+8
Here is the link for the answer to your query:
https://www.meritnation.com/ask-answer/question/show-that-the-cube-of-any-positive-integer-is-of-the-fo/real-numbers/1079774
https://www.meritnation.com/ask-answer/question/show-that-the-cube-of-any-positive-integer-is-of-the-fo/real-numbers/1079774