Sugar cubes are made in molds.

One of sugar's unique properties is that a liquid solution of it granulates when dried; it forms little cubical crystals or grains, which you see in granulated sugar. But if this is done in molds, it will form large solids in the shape of the mold, composed of lots of these grains stuck together. Sugar starts as a liquid, made from cane or beets or whatever.

Originally, starting in the 12th century or thereabouts, which this was discovered, these shapes were big cones (or loaf shapes in more primitive cases) called a sugarloaf, which weighed maybe ten pounds or so. Up until fairly recently, you'd buy a sugar loaf and snip off bits of it with a special pair of scissors called "sugar nips" when you wanted some. Then you could smash or grind or dissolve the little piece in your recipe. My great-grandparents bought (and sold; he was  grocer) their sugar this way at least part of the time, in the late 1800s and probably into the 1900s.

In the middle of the 19th century, a guy named Jakub Krystof Rad in what is now the Czech Republic invented the sugarcube by pouring the liquid into small square molds to dry. Supposedly he did so at the behest of his wife, who had cut herself once too often with her sugar nips.

Refs:

http://en.wikipedia.org/wiki/Sugar_loaf

Czech page on the invention of the sugarcube in the town of Dacice -- with photos of a sugarloaf with mold.