Question

A carton can hold 1'000 unit cubes that measure 1 inch by 1inch by 1 inch . How can describe the dimensions of the carton using unit cubes

Answer 1

You can't tell the dimensions from that information.
All you can say is that the length multiplied by the width,
and then that product multiplied by the height, is 1,000 .
But you can't say what the length or the width or the height is.

A few possibilities:

Length Width Height
1 1 1000
2 1 500
4 5 50
5 8 25
10 10 10
10 20 5

There are many more possibilities.