Also to make it much easier to grease the cube - if you do it as you stack the rows, you can get much more even distribution (and the cube will fly afterwards).
All Rubik's cubes have removable center tiles covers; they're usually difficult to remove without the help of an Xacto knife or similar. Under each tile is a screw; unscrewing these will allow you to take the center cubes off. After removing all the other non-center cubes, once you take the center 'cubes' off (they aren't really cubes, actually more like plates) it's easier to grease your cube up.
"They" don't, this model does
To be fair, most do.
To be meta-fair, most means those who have a brand name (those you could distinguish when you buy).