Question 64
Let $N$ be a positive integer. A cube $(2N+1) \times (2N+1) \times (2N+1)$ is made of $(2N+1)^3$ unit cubes; each unit cube is either black or white. It turned out that among any 8 unit cubes which form a cube $2 \times 2 \times 2$ the number of black unit cubes is not greater than 4. Find the greatest possible total number of black unit cubes.