8. (10 points) As shown in the figure, $A B C D$ is a parallelogram. $A E=2 E B$. If the area of triangle $C E F$ is $=1$. Then, the area of parallelogram $A B C D$ is $\qquad$ .
【Analysis】 $S_{\triangle A E F}: S_{\triangle C E F}=A F: F C=A E: D C=2: 3$, then $S_{\triangle A E F}=\frac{2}{3}, S_{\triangle A E C}=\frac{2}{3}+1=\frac{5}{3}$, similarly we can find $S_{\triangle A B C}$, and then the area of parallelogram $A B C D$.

【Solution】Solution: $S_{\triangle A E F}: S_{\triangle C E F}=A F: F C=A E: D C=2: 3$, then $S_{\triangle A E F}=\frac{2}{3}, S_{\triangle A E C}=\frac{2}{3}+1=\frac{5}{3}$, $S_{\triangle A E C}: S_{\triangle B E C}=A E: E B=2: 1$, then $S_{\triangle B E C}=\frac{5}{6}, S_{\triangle A B C}=\frac{5}{3}+\frac{5}{6}=\frac{5}{2}$,
$S_{\square A B C D}=2 S_{\triangle A B C}=5$
Answer: The area of parallelogram $A B C D$ is 5;
Therefore, the answer is: 5.