The given series is: 0, 2, 6, 12, 20, 30, ...

To find the sum of the first 20 terms of the series, we need to find a pattern or formula that relates the terms to each other.

The series seems to be increasing by 2, 4, 6, 8, 10, ... for each subsequent term. This can be seen by finding the differences between consecutive terms:

2 - 0 = 2
6 - 2 = 4
12 - 6 = 6
20 - 12 = 8
30 - 20 = 10

From the differences, we can see that the series is increasing by 2, 4, 6, 8, 10, ... for each subsequent term.

To find the sum of the first 20 terms, we can use the formula for the sum of an arithmetic series:

Sn = (n/2)(2a + (n-1)d)

where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, a = 0 (the first term), d = 2 (the common difference), and n = 20 (the number of terms).

Plugging these values into the formula, we get:

Sn = (20/2)(2(0) + (20-1)(2))
= 10(0 + 19(2))
= 10(0 + 38)
= 10(38)
= 380

Therefore, the sum of the first 20 terms of the series 0, 2, 6, 12, 20, 30, ... is 380.