What is the dimensions of a box 8 cubic feet

You can't tell. The volume doesn't tell you the dimensions. It only tells you

what the product of the three dimensions is, but not what anyone of them is.

There are an infinite number of different possibilities.

Example: Volume = 8 cubic feet

The dimensions of the box could be

Length = 2-ft, Width = 2-ft, Height = 2-ft

or

1 x 1 x 8

or

1 x 2 x 4

or

1 x 3 x 2-2/3

or

1 x 5 x 1.6

or

1 x 6 x 1-1/3

or

1 x 7 x 1-1/7

or

2 x 3 x 1-1/3

or

2 x 5 x 0.8

or

2 x 6 x 2/3

or

2 x 7 x 4/7

or

2 x 8 x 1/2

.

.

etc.