Draw a picture. Note that the shortest path will be up one side, across a face (say, the top), and down the opposite side. Note that this will be twice the length of one face. Use this to find the length of one face. Plug this value into the volume formula for a cube.

Use what you've learned in algebra about recognizing perfect-square trinomials. Deduce from this what the value of "a" must be, to create a perfect-square trinomial.

Draw a line. Reflect it in the x-axis. Look at the intersection point. See what you can conclude.