Volume · Superchallenge problem

A solid block of wood is $10$ cm long, $8$ cm wide and $6$ cm tall. A square tunnel $2$ cm wide and $2$ cm tall is cut straight through it from one end to the other, the long way. A second tunnel of the same size is cut straight through it from side to side, the short way, at the same height, so the two tunnels cross in the middle. What volume of wood is left, in cubic cm?