Let $b$ and $n$ be two positive integers. Is there are a general result which tell us when the polynomial $$1+x^{b}+x^{2b}+x^{3b}+\cdots+x^{nb}$$ is irreducible over the integers?

I know that $$1+x+\cdots+x^{n-1}$$ is irreducible if and only if $n$ is prime. I also know that $$1+x^n$$ is irreducible if and only if $n=2^k$ for some $k\geq 0$. However, I'd like to look at a linear sequence and know irreducibility before painstakingly looking for factors.

I've noticed that the $n$ above in the question must be even for otherwise we could factor out $1+x^b$. But other than that I haven't made much ground except for particular values of $n$. I'm kind of hoping for a 'one-fell-swoop' result, but if there isn't, I'd like a recommendation for a general plan of approach for determining irreducibility of these polynomials.

Any help is appreciated.