Learn Croatian: Poslali smo poruku bratu. - We sent the brother a message.

Because the brother is the person receiving the action (the indirect object), so the noun must be in the dative case. For most masculine nouns ending in a consonant like brat, you simply add -u to the end to make the dative form.

Both poruku and bratu end in -u. Are they in the same case?

No, they actually end in -u for completely different reasons! Poruku is the direct object (the thing being sent), which requires the accusative case; feminine nouns like poruka change their -a ending to -u in the accusative. Bratu is the indirect object (who it is sent to), which requires the dative case; masculine nouns add -u in the dative.

Where is the word for 'we' in this sentence?

In Croatian, subject pronouns like mi (we) are usually left out because the verb already tells you who is doing the action. The short helping verb smo is the form of 'to be' used for 'we', which makes it perfectly clear who sent the message.

Why does the main verb poslali end in -li?

This is the past tense ending for a plural subject. When 'we', 'you (plural)', or 'they' do something, and the group contains at least one male (or if the gender is unknown), the main verb gets the -li ending.