May 2017 Fiendish Function

The Fiendish Function posed during May 2017 had the following sample guesses and replies:

• GUESS
• REPLY
• 1
• 4
• 2
• 15
• 3
• 40
• 4
• 85
• 5
• 156
• 10
• 1111

The rule was: "Cube the number, add the original number squared, add the original number, then add one".

Suppose the guess was 13:

• Cube the number, giving 2197.
• Add the original number squared, giving 2366.
• Add the original number, giving 2379.
• Add one, giving 2380.

So the result is 2380.