The notion of a center of the Universe had been long existed. However the namesake has constantly changed throughout history from primordial guesses to an established fact.

For a brief period, it was even proposed that Milky Way's galactic center could be the center of Universe, but as of now, it's established that Universe has no center.
Another way of putting it is, every point in the Universe is expanding away from every other point i.e., like dots on the surface of a balloon when it is gradually filled. But remember, the surface of balloon itself is 3D space. What lies inside or outside the balloon is absolute nothingness. Not even space! Its what a rock thinks of!

Soundtrack: Walls by Opaqity (http://www.audiotool.com/track/walls-...)

A great start for Cosmology:
(http://map.gsfc.nasa.gov/universe/)