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

Yes.

The word "nuvem" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazil, the "e" is often more open, and the final "m" is a subtle nasalization of the preceding vowel. In Portugal, the "e" is often more closed or even reduced, and the nasalization of the "m" is typically more distinct, making the final syllable sound more heavily nasalized.

Brazilian Portuguese Examples:

1. Olhe para aquela nuvem escura! (Look at that dark cloud!)
2. A nuvem está passando muito rápido. (The cloud is passing very fast.)
3. Tem uma nuvem cobrindo o sol. (There is a cloud covering the sun.)
4. Tem muita nuvem no céu hoje. (There are many clouds in the sky today.)
5. Aquela nuvem parece um algodão doce. (That cloud looks like cotton candy.)

Continental Portuguese Examples:

1. Olha para aquela nuvem escura! (Look at that dark cloud!)
2. A nuvem está a passar muito depressa. (The cloud is passing very quickly.)
3. Há uma nuvem a tapar o sol. (There is a cloud covering the sun.)
4. Há muitas nuvens no céu hoje. (There are many clouds in the sky today.)
5. Aquela nuvem parece um pedaço de algodão. (That cloud looks like a piece of cotton.)