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• Is there a cuboid in which all edges and all diagonals are of integer length? (Perfect cuboid; 1719)
• Is there any even number which is not the sum of two primes?

In 3 dimensions, the positions of black cells can conveniently be displayed using
Graphics3D[Map[Cuboid[-Reverse[#]] &, Position[a, 1]]]

The exact cuboid form of the monolith in the movie 2001 was intended to suggest that it was an artifact.

In the movie 2001 a black cuboid with side ratios 1:4:9 detected on the Moon through its anomalous magnetic properties sends a radio pulse in response to sunlight.