I was testing out Rengar on a solo match against bots, everything seemed to be perfectly fine, until I went in a fight with Nasus bot and a Annie bot.

I noticed there was some sort of blue aura (box, maybe?) , I thought: "What? Is that a bug or just an item that gives him that weird looking thing?". I could not remember any item that would give him such aura. I killed him, Annie, and recalled to see the store.

I spent a while thinking, while waiting for Nasus to respawn. I went after him to see (also to take a print if the problem was still there). And so it was.

http://i49.tinypic.com/2d7anhz.png

I took another after running and recalling to base, while he was fighting Warwick.

http://i47.tinypic.com/2mnkxgj.png

So, while on base, I remembered that Nasus bot usually buys Sunfire cape, wich gives him a fire aura, and, to confirm, I bought it.

http://i50.tinypic.com/wbw64p.png

And there it was!

http://i45.tinypic.com/2hduzk4.png

So, what could it be? Can I do something to solve it (if it a problem with me)?

Thanks for the attention.

What you are seeing is called a declined particle, usually there is supposed to be fire that comes out of sunfire cape but you get blue box's because the particles are currently being updated or your game files are corrupt and need a repair. I suggest you open LoL and clicking repair this will organize all the files and make sure they are put into the right place and replace corrupt/missing files.
tl;dr run the repair tool that should fix your problem.

-Best of luck, Google

Google is correct, I would run a repair function via your LoL client and that should fix the problem. The only case where it would not be fixed is if Riot removed those files and were performing maintenance on them.