Well, if you look at the former Soviet Union, Russian culture is firmly entrenched there. If you travel around, you can use the Russian language, the elites all speak Russian and send their kids to Russian schools, read Russian literature, and in general watch Russian films and singers.

This was also the case in Ukraine to a large extent. That's where the Russian-speakers in Ukraine come from. Only a small percentage of them are actually ethnic Russians or other ethnicities that adopted Russian. Most of them are ethnic Ukrainians who started speaking Russian, since it was considered the "high" language, in a process similar to what happened in Ireland.

Paradoxically, it's Putin who has totally killed the influence of Russian culture outside of Russia. If he didn't believe himself to be the second coming of Peter the Great, then Russian culture would still be looked on as "high" culture in a lot of places.

PS: There is actually still a lot of Russian cultural influence even in Alaska. Many of the native Alaskan communities are Russian Orthodox, and some even spoke Russian until recent times.