<image>Observe: 
\[ 2^{2} - 1^{2} = (2 + 1)(2 - 1) = 2 + 1 = \dfrac{(1 + 2) \times 2}{2} = 3 \]
\[ 4^{2} - 3^{2} + 2^{2} - 1^{2} = (4 + 3)(4 - 3) + (2 + 1)(2 - 1) = 4 + 3 + 2 + 1 = \dfrac{(1 + 4) \times 4}{2} = 10 \]
\[ 6^{2} - 5^{2} + 4^{2} - 3^{2} + 2^{2} - 1^{2} = (6 + 5)(6 - 5) + (4 + 3)(4 - 3) + (2 + 1)(2 - 1) = 6 + 5 + 4 + 3 + 2 + 1 = \dfrac{(1 + 6) \times 6}{2} = 21 \]

Explore:
\[ (1) \ 8^{2} - 7^{2} + 6^{2} - 5^{2} + 4^{2} - 3^{2} + 2^{2} - 1^{2} = \_ \_ \_ \_ \_ \_ \_ \_ \_ \ \_ \ \]
(Write the answer directly);
\[ (2) \ (2n)^{2} - (2n - 1)^{2} + (2n - 2)^{2} - (2n - 3)^{2} + \ldots + 2^{2} - 1^{2} = \ \_ \_ \_ \_ \_ \_ \_ \_ \ \_ \ \]
(Write the answer directly);

Application:
\[ (3) \] As shown in the figure, \[ 2,018 \] circles are nested from small to large. Starting from the outside, shade alternating circles, with the outermost circle shaded. The radius of the outermost circle is \[ 2,018 \ \text{cm} \], followed by \[ 2,017 \ \text{cm} \], \[ 2,016 \ \text{cm} \], \[ \ldots \], \[ 1 \ \text{cm} \]. What is the total area of all shaded regions in this figure? (Keep the result in \[ \pi \)) 