Thank you for your answer. I understand that it is not possible to have a general solution for such problems (although it would be good). I experimented with another simple case without any result. For example consider the simple sequence 1, 3, 4, 7, 11, 18, 29, ???, 76, 123. Here the obvious pattern is that the third number is the addition of the previous two i.e. 1+3=4 the forth 4+3=7 etc.

ClearAll["`*"];
y[1] = 1;
y[2] = 3;
y[n_] := y[n] = (y[n - 1] + y[n - 2])
data = Table[{i, y[i]}, {i, {1, 2, 3, 4, 5, 6, 7, 9, 10}}]
FindFormula[data][8]
Interpolation[data][8.]

None of the suggested solutions produce the correct answer 47 neither reveals the hidden pattern.

Great answers as always! Thanks.

Agreed. However, my biases are that many of those who post such "puzzles" on the internet don't understand that it is possible to put any value in for the missing number (which might not even be an integer and could be a complex number or anything else).

What one is looking for is a simple/parsimonious function to reproduce the (usually) integers given. One has to look for such simple functions to pass college entrance exams as such "puzzles" are included. (Well, 40 years ago they were.)

You could try FindSequenceFunction on subset that is contiguous:

FindSequenceFunction[{1, 8, 27, 64, 125}]
(* #1^3 & *)

Then use that function to predict the rest. If the predictions for the remaining known numbers match up, then you're home free.

If one doesn't have Mathematica, you can try https://oeis.org/.

Thank you very much for the answer. I was completely unaware that there is a function FindFormula.