When my husband told me about it, he explained it was not precisely sugar "cubes." It was more like sugar chunks. They would break up a block of sugar and hold a chunk between their teeth. These days, I think it is more cube than chunk. But, they also have granulated like we do as well.

And, it's apparently not that uncommon in the region. He shared this when we saw an old man doing it in a documentary (on Egyptian Arabs, I think). And, I he shared that was how some folks did that in Iran.