The volume of a cube is given by;
(One length side of the cube)³ - remember all sides of a cube are the same, just like how both sides of a square are the same. This is essentially the area of the square at the base, multiplied by the height of the cube.
Hence why we that that, for example 4³, is "4 cubed"
So we know that;
volume = (side length)³
Alternatively we could say that;
Side length = ∛volume
(we have just found the cube root of both sides here, remember we can do what we like to an equation, as long as we do the same to both sides)
Because we cubed side length to get volume, side length must be the cubic root of the volume, the ∛.
We know that the volume is 1000 cubic feet, so;
Side length = ∛1000
∛1000 = 10
So one side length is 10 feet.