Missing number in the series 9, ____, 6561, 43046721 is: 81 25 62 31 18

Missing number in the series is:

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Given series: 9,2, 6561, 43046721
We need to determine the missing number in the series.
First, we note that $43046721=6561\cdot 6561={6561}^{2}$ and thus we suspect that each term is the square of the next term.
Let us determine the square of the first term 9:
${9}^{2}=81$
Thus we suspect that the missing term is 81, which is confirmed by the fact that ${81}^{2}—6561$.