I believe Charles Darwin wrote about honeycombs in his book "The Origin of the Species". He wrote that the hexagons shapes built by the bees is proved to be the most efficient way of storing the honey (I'm assuming it was proved by the mathematicians of the era, or perhaps earlier. How valid is the proof? I have no idea).

He explained how they build it - which is quite amazing. Each bee digs in rotation, to form a sphere. Whenever two bees dig long and deep enough to meet, they build a thin wall.

Again, as for the proof of this optimum and its validity - I am clueless (geometry was never my strong side). If anyone can fill this part in - I'd be happy to read it myself.