January 2018 Fiendish Function

The Fiendish Function posed during January 2018 had the following sample guesses and replies:

• GUESS
• REPLY
• 1
• 2
• 2
• 9
• 3
• 28
• 4
• 65
• 5
• 126
• 10
• 2

The rule was: "Add the cubes of the number's digits together, then add one".

Suppose the guess was 24:

• Take the number's digits, giving 2, 4
• Cube them, giving 8, 64
• Add these together, giving 72.
• Add one, giving 73.

So the result is 73.