Question 34692
Sketch the cube.  Sketch in the 4sqrt3 diagonal
Let "x" be all the sides of the cube.
The diagonal of the base is xsqrt2
The 4sqrt3 diagonal is the hypotenuse of a triangle whose other 
sides are "x" and 4sqrt3.
Then x^2+(xsqrt2)^2 = (4sqrt3)^2
x^2+2x^2 = 16(3)
3x^2=16(3)
x^2=16
x=4 (the side of the cube)
Volume = side^3 = 64 cu cm
Cheers,
Stan H.