Learn Polish: Piję kawę bez mleka i bez cukru. - I drink coffee without milk and without sugar.

The preposition bez (without) always requires the noun that follows it to take the Genitive case. So, the neuter noun mleko takes the ending -a to become mleka, and the masculine noun cukier changes to cukru.

Where did the letter 'e' go in cukru, and why doesn't it end in -a like some masculine nouns?

The word cukier has a 'fleeting e,' meaning the 'e' drops out when endings are added (leaving the base cukr-). For the ending itself, masculine inanimate nouns in the Genitive take either -a or -u. Uncountable substances and materials (like sugar, sand, or juice) generally take the -u ending.

If this lesson is about the Genitive case, why is coffee written as kawę instead of the Genitive kawy?

Kawa is the direct object of the positive verb piję (I drink), so it needs to be in the Accusative case (kawę). The preposition bez only affects the nouns that come directly after it, not the words before it.

Is it necessary to repeat the word bez before cukru?