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

Yes

The word "nunca" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the nasal vowel "un" is typically more open and the rhythm of the word is more fluid. In Continental Portuguese, the pronunciation is often more closed, and the vowels can be more compressed or "swallowed" depending on the regional accent.

Brazilian Portuguese Examples

1. Eu nunca comi isso. (I have never eaten that.)
2. Ela nunca faz o dever de casa. (She never does her homework.)
3. Você nunca me liga! (You never call me!)
4. Nunca vi um cachorro tão grande. (I've never seen such a big dog.)
5. A gente nunca vai desistir. (We are never going to give up.)

Continental Portuguese Examples

1. Eu nunca o comi. (I have never eaten it.)
2. Ela nunca faz os trabalhos de casa. (She never does her homework.)
3. Tu nunca me ligas! (You never call me!)
4. Nunca vi um cão tão grande. (I've never seen such a big dog.)
5. Nós nunca desistiremos. (We will never give up.)