Is the word cuba the same in Brazilian and European Portuguese?

Yes

The word "cuba" is identical in both Brazilian and Continental Portuguese regarding its spelling, grammar, and meaning. It functions as a proper noun (referring to the country Cuba) and as a common noun (referring to a large basin, vat, or the bowl/basin of a sink). The only difference between the two dialects is the pronunciation, specifically the phonetic realization of the vowels.

Brazilian Portuguese Examples

1. Eu pretendo viajar para Cuba no próximo ano. (I intend to travel to Cuba next year.)
2. A cuba da pia está entupida. (The sink basin is clogged.)
3. Ele limpou a cuba de metal com muito cuidado. (He cleaned the metal tub very carefully.)
4. Cuba é um país localizado no Caribe. (Cuba is a country located in the Caribbean.)
5. Preciso trocar a cuba do banheiro. (I need to replace the bathroom sink.)

Portuguese (PT-PT) Examples

1. Eu pretendo viajar para Cuba no próximo ano. (I intend to travel to Cuba next year.)
2. A cuba do lavatório está entupida. (The bathroom sink basin is clogged.)
3. Ele limpou a cuba de metal com muito cuidado. (He cleaned the metal tub very carefully.)
4. Cuba é um país localizado no Caribe. (Cuba is a country located in the Caribbean.)
5. Preciso trocar a cuba da casa de banho. (I need to replace the bathroom sink.)