what happens if you freeze cream while shaking
A. It's not a great idea. Cream tends to separate when frozen, and while you can freeze a carton of cream (double-wrapping in freezer bags is recommended), you can also shake it thoroughly after it thaws to reblend it (although it will not be as good as new).
With cream cubes, you're likely to have a block of frozen water on the bottom and a crumbly layer of butterfat/milk solids on top. Jumble them around in a freezer bag and you'll wind up with a mess that's not very easy to use.