"Six years, sixty years"
Translation:Шість років, шістдесят років
Mainly in song and poetry, idiomatic expressions. Also its forms are part of some words and phrases. Століття (century), літня пані (elderly lady). There bound to be more, that's all I could think from top of my head. I believe its etymology is similar to Russian, from the word for summer (літо), it has to be plural form. I could be completely off though :)
In all modern usage and contexts as far as using word for year/years stick with рік/роки and you'll be fine.