930
-9
The greatest 3-digit number is 999. 9+9+9 = 27 The sum of the greatest 3-digit number is 27.
Nine hundred thirty (930) is the highest three digit number whose digits have a sum of 12. 9+3+0=12. Any numbers higher than that will give you an sum greater than 12.
99999
123
It is: 999 => 9+9+9 = 27 => 2+7 => 9
27
3201
44
36
27, whose cube is 19683
940