3. A large cube is formed by $8 \times 8 \times 8$ unit cubes. How many lines can pass through the centers of 8 unit cubes?
(Prompt: Add another layer of unit cubes on the outside, prove that the line is in one-to-one correspondence with the added unit cubes. Answer: $\left.\frac{1}{2}\left(10^{3}-8^{3}\right)\right)$