Last year my age was a square number. Next year my age will be a cube number. What is my present age?

Find a list of squares and cubes:

Cubes: 1, 8, 27

Squares: 1, 4, 9, 16, 25

Notice '25' and '27'.

If his age was '25' last year, it would be a perfect square 5 * 5. If his age next year will be '27', it will be a cube, 3 * 3 * 3.

So his age now is 26.

He is 26 now BC last year he was 25 (perfect square). Next year he will be 27 (Cube).