I am trying to gain british nationality for my cuban girlfriend. If we
marry and she lives in the UK for three years then this is possible.
Are there any other ways of achieving British nationality for her?

I note that you head your question "Immigration to the UK from Cuba",
though you then ask about UK nationality, which is several steps down
the road. Assming your girlfriend is in Cuba at present, I would have
thought the first problem is how she gets out of the country, since
the Cuban Government strictly controls travel abroad. Then, of course,
she would need a UK visa to enter the country, and this might be
awkward, since (a) the visa authorities might be sceptical if she said
she wanted to go to the UK for a short touristic visit; and (b) they
would almost certainly deny her a visa if she said she wanted to stay
in the UK indefinitely. One course which occurs to me, though it would
not get over the problem of getting permission to leave Cuba, would be
for you to get married in Cuba, though this might also be banned in
Cuba. Sorry to be so negative; and don't take my comments as the final
word - I may be quite wrong.

Thanks for your thoughts, i realise that UK immigration from outside
the EU is a very difficult task and I understand where you're coming
from. I have already sent an invitation letter to the Cuban embassy in
London which gives Rosy ( my girlfriend ) permission to leave Cuba
from a cuban perspective for the next 11 months. As far as getting her
a tourist visa for the UK I have yet to cross this hurdle, although I
had always assumed it would be possible.

The terms of the invitation state that I am fully responsible for her
financially while she is here which I think means she would not be
able to seek asylum as she would not qualify. Thanks again, if you
have any more thoughts please don't hesitate to post.

Enrollment in a language school is the usual trick.

Be careful that you are not just a (disposable) meal ticket.

Bluebabboon, If you aren't already familiar with it, you may find the
following UK Gov info on immigration & visas etc useful -
http://www.ukimmigration.com/family/uk_spouse_visa.htm

thanks i'll take a look.