131 On each face of an opaque cube, a natural number is written. If several (one, two, or three) faces of the cube can be seen at the same time, then find the sum of the numbers on these faces. Using this method, the maximum number of different sums that can be obtained is $\qquad$.
131 26. We can see a single face (6 cases), two adjacent faces (12 cases), or we can also see three faces that share a common vertex (8 cases), thus yielding a total of 26 sums. We can appropriately fill in the numbers on each face so that all 26 sums are distinct (for example, we can fill the 6 faces with $\left.1,10,10^{2}, 10^{3}, 10^{4}, 10^{5}\right)$ .