8. (10 points) The difference between the minimum value of the sum of the squares of ten different odd numbers and the remainder when this minimum value is divided by 4 is $\qquad$
(Note: The product of the same two natural numbers is called the square of this natural number, such as $1 \times 1=1^{2}, 2 \times 2=2^{2}, 3 \times 3$ $=3^{3}$, and so on)
8. (10 points) The difference between the minimum value of the sum of the squares of ten different odd numbers and the remainder when this minimum value is divided by 4 is $\qquad$ 1328.
(Note: The product of the same two natural numbers is called the square of this natural number, such as $1 \times 1=1^{2}, 2 \times 2=2^{2}, 3 \times 3=3^{2}$, and so on.)

[Analysis] The minimum value of the sum of the squares of ten different odd numbers, i.e., starting from 1 to 19, find the sum of the squares of 10 different odd numbers from $1 \sim 19$, then find the remainder when this minimum value is divided by 4, and finally subtract this remainder from the sum of the squares of the 10 different odd numbers.

[Solution] Solution: $1^{2}+3^{2}+5^{2}+7^{2}+9^{2}+11^{2}+13^{2}+15^{2}+17^{2}+19^{2}$,
$$
\begin{array}{l}
=1+9+25+49+81+121+169+225+289+361, \\
=1330 \\
1330 \div 4=332 \cdots 2, \\
1330-2=1328 ;
\end{array}
$$

Therefore, the answer is: 1328.