Open excel (or any other spreadsheet app) or - at a push - the calculator app.

Type in 45 * 45. You will get 2025. Then try 44 * 44 and 46 * 46. You don't need a PhD to be able to do that :)

Then you can use the same app to add up 1 - 9 and get 45, which will verify most of the post.

The cube thing is a little more complex, but you should be able to work it out using the multiply and the memory function.

(I checked it before I posted it :))