Yes you can mail cigarettes through USPS or even UPS or FedEx.
The USPS has more restrictions on what you can mail and when you mail cigarettes they have more restrictions on them than UPS or FedEx do.
If you need to mail cigarettes to somebody you should mail them through UPS or FedEx and really FedEx or UPS will not really know you're mailing the cigarettes.
They will just think you're shipping any old package.
I have shipped some cigarettes to a friend out of state through USPS and they never said anything.
I just placed the cigarettes in a brown box and mailed it as a normal package and it shipped through the USPS just fine.
However if you're mailing cigarettes overseas then it likely won't make it through customs.