8. (10 points) Definition: $\triangle a=a+(a+1)+(a+2)+\cdots+(2 a-2)+(2 a-1)$, for example: $\triangle 5=5+6+7+8+9$, then, $\triangle 1+\triangle 2+\triangle 3+\cdots+\triangle 19+\triangle 20$ the calculation result is $\qquad$ .
【Solution】Solution: According to the analysis, fill all these numbers into a table for easy observation, as shown in the figure: the 1st row represents $\triangle 1$, the 2nd row represents $\triangle 2$, the 3rd row represents $\triangle 3$, and the 20th row represents $\triangle 20$. For convenience of observation, rotate this table $135^{\circ}$ clockwise, as shown in Figure 2. At this point, the average of each row is 20, and there are $1+2+\cdots+20=210$ numbers in the table, so the sum is $210 \times 20=4200$