I'm assuming that a coffee spoon is another word for a teaspoon where I'm from, if that assumption is invalid then this answer will be incorrect, but a teaspoon is ~4.2-5g of sugar depending on the size of the teaspoon.
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Around 10-12 grams, depending on how big the soup spoon is (the sizing is not standardised, unlike tablespoons/teaspoons). It also depends on how heaped the sugar is on the spoon.
A cup of plain coffee does not contain any naturally-occurring sugars. Any sugar would have to be added.