The sum to 20 terms of the series $$2 \cdot 2^2 - 3^2 + 2 \cdot 4^2 - 5^2 + 2 \cdot 6^2 - \ldots$$ is equal to _____.

We need the sum to 20 terms of the series $$2 \cdot 2^2 - 3^2 + 2 \cdot 4^2 - 5^2 + 2 \cdot 6^2 - 7^2 + \cdots$$

The 20 terms form 10 pairs. The $$k$$-th pair ($$k = 1, 2, \ldots, 10$$) is:

$$2(2k)^2 - (2k+1)^2$$

Expanding:

$$2(2k)^2 - (2k+1)^2 = 8k^2 - (4k^2 + 4k + 1) = 4k^2 - 4k - 1$$

The total sum is:

$$S = \sum_{k=1}^{10}(4k^2 - 4k - 1) = 4\sum_{k=1}^{10} k^2 - 4\sum_{k=1}^{10} k - 10$$

Using standard formulas:

$$\sum_{k=1}^{10} k^2 = \frac{10 \times 11 \times 21}{6} = 385$$

$$\sum_{k=1}^{10} k = \frac{10 \times 11}{2} = 55$$

Therefore:

$$S = 4(385) - 4(55) - 10 = 1540 - 220 - 10 = 1310$$

The answer is $$\boxed{1310}$$.