So you have a very tight store-bought cube...
I have a store bought cube and it is very loose and fast. But it once used to be ridiculously tight.
What I did was sand down the corners and edge pieces, break the cube in, and then lube the cube using shock oil (a silicon based oil lubricant). Simply lubing the cube won't help as much.
Cubes are usually very resilient but are also very weak to any petroleum-based lubricants, so try to avoid petroleum jelly.
Here are the steps I recommend based on my experience with the tight store cube:
1. Twist your cube for 1+ weeks like crazy. This "breaks in" the pieces and the natural grinding of plastic pieces makes your cube a bit faster.
2. Go to this
YouTube video, sand your cube. Your cube will become a bit faster and it will be a bit easier to cut corners.
3. Play with your cube for another 1+ weeks, then watch this
Youtube video on how to break in your cube. Now you will be able to cut corners and turn your cube much faster! Be careful though, you might accidentally break your cube, and "breaking in" too much can be negative, because it might make your cube too loose. Keep in mind that once you make a store bought cube loose, there is no going back to tight cube.
4. Lube your cube. If you choose to use shock oil like me, just pry open an edge of your cube and put ONE drop of the oil into the cube. But if you want to use silicon spray like many people, then watch this
Youtube video.
Now your cube will fly! BE CAREFUL THOUGH not to put too much lube regardless of which lube you decide to use. Too much will make your cube sticky.