Acarton can hold 1000 unit cubes that measure 1" x 1" x 1" what are the dimensions of the carton using unit cubes

The volume of the carton doesn't tell you the dimensions.

Without cutting up any of the little cubies, the 1000 of them could be
packed into a carton with any of these sets of dimensions:

1 x 1 x 1000
1 x 2 x 500
1 x 4 x 250
1 x 5 x 200
1 x 8 x 125
1 x 10 x 100
1 x 20 x 50
1 x 25 x 40

2 x 2 x 250
2 x 4 x 125
2 x 5 x 100
2 x 10 x 50
2 x 20 x 25

4 x 5 x 50 
4 x 10 x 25
4 x 25 x 100
  
5 x 5 x 40
5 x 8 x 25
5 x 10 x 20

10 x 10 x 10