7.3. A cube is placed on a table. Can 8 numbers; $1,2, \ldots, 8$, be placed at its vertices so that the following two conditions are met: 1) if the two numbers at the ends of each vertical edge are added, then all four sums are the same; 2) the sum of the numbers on the top face is equal to the sum of the numbers on the bottom face?
Answer: Yes. Instruction Let's provide an example. Place the numbers $1,7,6,4$ at the vertices of the square ABCD of the lower base, and above them, at the vertices of the square $A_{1} B_{1} C_{1} D_{1}$, place the numbers $8,2,3,5$. Then the sums at the vertices of both squares are 18 each. On each of the vertical edges, the sum is 9.