A solid wooden cube of edge 10 cm has a small cube of edge 3 cm sawn away from one of its corners. What is the surface area of the solid that remains, in square cm?

The original cube has $6\times 10^2=600$ sq cm. Cutting a cube out of a CORNER takes away three squares of $3\times 3$ that were part of the outside, and at the same instant exposes three fresh squares of $3\times 3$ inside the notch. Since $3\times 9$ is removed and $3\times 9$ is added, the surface area is unchanged at 600 sq cm. The trap 573 = 600 - 27 removes the three old squares and overlooks the three new ones; 627 = 600 + 27 adds the new ones without removing the old; 546 = 600 - 54 strips off all six faces of the little cube, though three of them were never on the outside to begin with.