The way I was shown to make a cuban shot
is to fill the basket
like you would for a normal shot of espresso, tamp
it, and pour in a packet or two of natural sugar
(in the brown packets), and run the shot through your espresso machine like normal.
The sugar does two things from what I can tell: 1. It removes the bitterness of the espresso (and I don't mean it sweetens it. The sugar dissolves and runs through the coffee, and causes the hot water to pick up less of the oils and bitterness out of the grounds.) and 2. It sweetens the shot (This part is from the sugar :) Quite the delectable treat, and I prefer it much to a normal shot, but many american places have never even hard of a cafe cubano, let alone know how to make one.
If you work at a coffee shop and make one, you should backwash your machine as soon as possible to clean any residue sugar. This is so the sugar doesn't gum up the filter and inner-workings of the espresso machine.