My Little Pony: Friendship is Magic - Image #290,789

While we can't say that they are immortal, we can safely say that they can live a damn long time (upwards of a thousand years).
However, this creates a terrible scenario where Cadence gets married to Shining Armor and is forced to watched the world and her husband age and eventually die around her while she lives on with Celestia and Luna.
And yes, I can make anything sad. It's my curse.

Cadence is, quite clearly, not as powerful as Celestia and Luna.

Therefore, it's safe to assume she is not a demigod or god, as the twins are. So, since there is no evidence supporting her having immortality, or even having a longer life, she is not, until further notice.

Alicorns=/=gods

Cadence, being Celestia's niece, is just as much a princess as Blueblood is a prince. They're related to the twins due to cousins, uncles, aunts, etc. These relatives were probably alicorns, but, due to cross-breeding with other races, are much rarer.

So, while alicorns are very hard to find, they do exist. The only strengths they have over other ponies is having both wings and magic. Cadence doesn't have the magic power of Twilight, or the flight skills of Rainbow Dash, but she has weaker versions of both.