Question 33556
The volume of a cube is given by:{{{V = s^3}}} where s is the length of one edge of the cube.

A cube with a volume of 64 cubic feet has an edge of length (the cube-root of 64)4 feet.
A cube with a volume of 343 cubic feet has an edge of (the cube-root of 343) 7 feet.

The scale factor of the smaller cube to the larger cube is then:
{{{4/7}}} or 
4 to 7 or 
4:7