When the largest sphere possible is carved out of a cube..........the side of the cube is the diameter of the sphere

So the diameter of the cube is 7cm and the radius is 7/2=3.5cm
And side of the cube = 7cm

The volume of the wood left after carving out the sphere is volume of cube- volume of the sphere

volume of the sphere= 4/3π r^{3}
 volume of the cube=7*7*

volume of the leftover wood= 343-179=

The volume of the leftover wood is                         
 wooden cube of side 7cm is the diameter of the sphere.
therefore radius =7/2cm
the remaining volume is =volume of cube-volume of sphere