3.85 On each face of an opaque cube, write down 1 natural number. If some faces of the cube can be seen at the same time, record the sum of the natural numbers written on these faces.
(1) Prove that it is possible to write natural numbers on each face of the cube so that all these sums are distinct;
(2) When all these sums are distinct, find the minimum value of the largest sum among these sums.
［Solution］Obviously, one can see only 1 face at a time, or 2 faces sharing 1 common edge, or 3 faces sharing 1 common vertex. Therefore, a total of 26 sums can be obtained. When the numbers written on each face are as shown in the figure on the right, it is easy to verify that the 26 sums are all different, and the largest sum is 26. Since all these sums are natural numbers, it is known that the largest sum must be no less than 26. Therefore, the minimum value of the largest sum is 26.