The largest three-digit number whose digits sum to 13 is 940. This is because the number must start with the highest possible digit, which is 9. To achieve a digit sum of 13, the next two digits must total 4, and the highest combination is 4 and 0, giving us 940.
17, 53, 71
940
27, whose cube is 19683
1+2+3=6 1x2x3=6 123
The number is 81.
930
123
27
44
36
17, 53, 71
940
27, whose cube is 19683
36
-9
1+2+3=6 1x2x3=6 123
The number is 81.