Look at the prime factorization. If all the factors have powers that are multiples of 6, then the number is a square and a cube. If they are multiples of 3, then a cube; if multiples of 2, then a square.
1000 = 2³·5³ . . . . a perfect cube
4 = 2² . . . . a perfect square
120 = 2³·3·5 . . . . none of the above (not a square or a cube)
36 = 2²·3² . . . . a perfect square
100 = 2²·5² . . . . a perfect square
49 = 7² . . . . a perfect square
125 = 5³ . . . . a perfect cube
25 = 5² . . . . a perfect square
