By analogy, think about what happens to the edges when you go up a dimension. You always make two copies of the object and connect along the same number of edges as there were corners. That is, we made two copies of a single point and joined them with a single edge, to make a line segment. Then we took two line segments, each with 1 edge and 2 corners, and used 2 edges to connect them, thereby creating a square which has 4 edges. Next, we took two copies of the square, each with 4 corners and 4 edges, and connected them using 4 edges, giving us a cube, which has 2*4+4 edges. Then the hypercube should have 16 corners, and taking two cubes, each with 12 edges and 8 corners, we use 8 edges to connect the two cubes, so we get a hypercube with 32 edges.

Now, I've said here that we take two cubes to make a hypercube, by connecting the two cubes, but above I said there are 8 cubes used to construct a hypercube. Can you see why?