The cube that you are describing is not a Rubik's
brand cube. It is made by another company. The pieces of the puzzle you have probably look something like this.
However, genuine Rubik's cubes, like the ones made by Hasbro and Winning Moves, look different. Here is a picture of a Rubik's DIY cube. (It is part of a picture
from this website.)
Most non-Rubik's 3x3x3 cubes look the same. Sometimes it can be hard to tell what company made them.
As for lubricating the cube, like Sharkretriver said, it will help the puzzle turn smoother. It doesn't matter what brand the cube is.