Prove or disprove the following statement: ‘No cube of an integer has 2 as its units digit.’

This is a very standard proof question for the C3 exam. The first thing that I would do when I see wordy proof statements like this is to make sure I understand what it means. Maybe writing out the statement more simply might help. So for this statement: n^3 never ends in 2. The second thing is just to try a few examples. With this statement, the example you should start with are nice and clear:
1^3=1 2^3=8 3^3=27 4^3=64 5^3=125 So far we haven't seen a number ending in two, and we haven't seen a pattern with the final digits yet, so we must continue.  6^3=216 7^3=343 8^3=512 So by finding a number where the statement is not true, we have found a counter-example so we have disproved it.