Unlike normal charges interest begins accruing on cash advances immediately. On a normal charge you're not charged interest until the grace period is over.
You paid interest from the time the cash advance occurred until the statement closing date. Between the statement closing date and the bill due date you were still accruing interest on that cash advance balance which is now appearing on new statement.
Cash advance should really be avoided primarily because the interest is immediate, and a payment is credited to the account rather than toward a specific charge or cash advance (though IIRC payments should credit the highest rate first by law in the US now). Some banks will not let you pay the cash advance specifically, even over the phone.
In a normal charge situation, where you've been paying in full every month and not paying any interest, you will not begin accruing interest until after you let a balance remain past the grace period which is typically the statement due date. That's why you can just pay in full at the end of the month and not receive interest charges. Cash advances will accrue interest from the date the cash is sent until it's paid in full regardless of grace periods or statement dates.
Consider this situation, I'm making these dates up but this is generally how it works. Your statement period is 12/15/2015 through 1/14/2016, the statement is due on 2/10/2016. You made the cash advance on 1/1/2016. You paid it on the 2/10/2016 payment. You weren't being charged multiple months of interest, you just paid the interest that accrued from 1/1/2016 through 2/10/2016 (the date the cash advance occurred all the way through the date it was paid in full) over two consecutive statements.