8. (10 points) Each letter in the table represents a number, and different letters represent different numbers. The leading digit of each number cannot be zero. Each row from left to right forms an arithmetic sequence, and each column from top to bottom also forms an arithmetic sequence. Therefore, the five-digit number $\overline{\mathrm{CDEFG}}=$ $\qquad$
\begin{tabular}{|l|l|l|}
\hline$A$ & $B A$ & $A A$ \\
\hline
\end{tabular}
\begin{tabular}{|c|c|c|}
\hline$A B$ & $C A$ & $E F$ \\
\hline$C D$ & $G A$ & $B D C$ \\
\hline
\end{tabular}
【Solution】Solution: (1) Since $A, B A, A A$ form an arithmetic sequence,
so $A + A A = 2 B A$,
so $A + 11 A = 2 \times (10 B + A)$,
so $12 A = 20 B + 2 A$,
simplifying, we get $B = 0.5 A$.
(2) Since $A, A B, C D$ form an arithmetic sequence,
so $A + C D = 2 A B$,
so $A + C D = 2 \times (10 A + 0.5 A)$,
simplifying, we get: $C D = 20 A$,
so $D = 0, C = 2 A$,
since $0 < 2 A < 10$,
so $A = 1, 2, 3$ or 4, combining with $B = 0.5 A$, then $A = 4$ or 2, $B = 2$ or 1.
(3) Since $A B, C A, E F$ form an arithmetic sequence,
so $A B + E F = 2 C A$,
so $10 A + 0.5 A + E F = 2 \times (20 A + A)$,
simplifying, we get: $E F = 31.5 A$, only when $A = 2$ it satisfies.
(4) Since $B A, C A, G A$ form an arithmetic sequence,

so $B A + G A = 2 C A$,
so $5 A + A + 10 G + A = 2 \times (20 A + A)$,
simplifying, we get: $G = 3.5 A = 7$,
so $A = 2, C = 2 \times 2 = 4, D = 0, E F = 31.5 \times 2 = 63, G = 7$, thus the five-digit number $\overline{\mathrm{CDEFG}} = 40637$.

Therefore, the answer is: 40637.