Imagine a cube with three circular holes cut from one face to another, when the width of the circles are the same width of the cube. If the width of the cube is 'x', what (with respect to x) is the volume left?

Is it anything like the answer to my formula:

e=(x sqrt2 - x)/(2 sqrt2)
f=x/(2 sqrt2)

Volume = 8(e^3 + (50316387 f e^2)/90474462)

The problem with a solution appears in

M. Moore, Symmetrical Intersections of right circular cylinders, Mathematical Gazette, No 405, 1974

The answer is x3(sqrt(2) - 1).

I have not seen the paper itself (the reference is from D. Wells' The Penguin Dictionary of Curious and Interseting Geometry), but in a recent Am Math Monthly (v 111, n 6. Jun-July 2004, pp 496-508) there is an article by T. Apostol and M. Mnatsakanian, A fresh Look at the Method of Archimedes that shows an approach to solving a similar problem (intersection of semicylinders.)