4. Arrange all positive odd numbers in ascending order, then take the first number as $a_{1}$, the sum of the next two numbers as $a_{2}$, and the sum of the next three numbers as $a_{3}$, and so on, to get the sequence $\left\{a_{n}\right\}$, i.e., $a_{1}=1, a_{2}=3+5, a_{3}=7+9+11, \cdots$, then the sum of the first 20 terms of $\left\{a_{n}\right\}$, $a_{1}+a_{2}+\cdots+a_{20}=$ $\qquad$.
The first 20 terms of $\left\{a_{n}\right\}$ contain a total of $1+2+3+\cdots+20=210$ odd numbers, so $a_{1}+a_{2}+\cdots+a_{20}=210^{2}=44100$.