1,000,000 Cubes

You have \(1,000,000\) cubes of eight different colors, and you arrange them into a \(2 \times 2 \times 250,000\) cuboid, so that no two cubes of the same color meet at a side, an edge or a vertex.

Is it possible for any two of the eight corner cubes of the \(2 \times 2 \times 250,000\) cuboid to share the same color?

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