The faces of a cube contain the numbers 1,2,3,4,5,6 such that the sum of the numbers on each pair of opposite faces is 7. For each of the cube’s eight corners, we multiply the three numbers on the faces incident to that corner, and write down its value. (In the diagram, the value of the indicated corner is 1 \times 2 \times 3=6.) What is the sum of the eight values assigned to the cube’s corners?
