No, it is not common cucumber

Here's another picture it sure is growing and hooking into other plants like a cucumber!!

It's definitely not a cucumber. After a quick search it looks like Japanese hops.

Rodney

Here is a link that might be useful: Japanese Hop Images

Japanese Hops is considered invasive.

Here is a link that might be useful: http://www.nps.gov/plants/alien/fact/huja1.htm

Yep.....its hops vine. Its growing all over my property. :(