我们知道：
1^2 + 2^2 + ... + 10^2 = 330
方法如下：
10^2 - 5^2 = 75
9^2 - 4^2 = 65
8^2 - 3^2 = 55
7^2 - 2^2 = 45
6^2 - 1^2 = 35
5^2 - 0^2 = 25
上面是300。the rest is: 4^2 + 3^2 + 2^2 + 1^2, which is 30.
So the total is 330

Similar way for 1^2 + 2^2 + ... + 20^2:

20^2 - 10^2 = 300
19^2 - 9^2 = 280
....
11^2 - 1^2 = 120
10^2 - 0^2 = 100

which is 5 x 400 + 200

So the total is 2200 + 330 - 100 which is 2430.

I guess everyone understands the above calculation. My son taught me this :)