What a difficult question!
Of course, both are correct, as Sosia said. But they are used differently.
The most common, no doubt (at least here, in Spain) is
para siempre.
Por siempre is only for really advanced Spanish speakers, as not every
colocación (I don't know what to call this in English, ¡t's a technical term) is always accepted.
Maybe
por siempre is a literary usage of
para siempre that has overcome other usages (but I cannot state this, I should make a research on it).
Anyway,
por siempre conveys the idea not only of
forever but also of
continuously, and you can use it also in the past, meanwhile you can use
para siempre only in the future.
- He vivido aquí (por) siempre.
- He vivido aquí para siempre.
- Me voy de aquí para siempre.
- Me voy de aquí por siempre
Hey, this is interesting. We'll have to check it!