10. (5 points) According to the pattern shown in the figure, deduce that $M=$

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【Solution】Solution: According to the problem, we have:
First, observe the pattern: $12+3=15$;
$15+5=20 ; \cdots$ Each square plus the circle equals the next number.
At the same time, we notice $20=12+3+5$
$$
27=12+3+5+7
$$

Summarizing the pattern, the numbers in the circles form an arithmetic sequence with the first term 3 and a common difference of 2. Each subsequent square is the sum of all previous numbers.
$$
M=12+3+5+7+9+11+\cdots+81 .
$$

The number of terms is $\frac{81-3}{2}+1=40$.
$$
\begin{array}{l}
M=12+\frac{3+81}{2} \times 40 \\
=12+84 \times 20 \\
=1692
\end{array}
$$

Therefore, the answer is: 1692