Let the six faces of a cube be numbered 1, 2, 3, 4, 5, 6 in such a way that the 3 pairs $$(1,6)$$, $$(2,5)$$, $$(3,4)$$ lie on opposite faces of the cube. At each vertex of the cube, the product of the three numbers on the three faces containing the vertex is written. What is the sum of all the eight numbers written at the eight vertices of the cube?