They are modular. Wooden pegs come with for stacking. You know, pegs in the hole, line up the top one, slot it in, repeat...
I have had no problems but then stacking could be a challenge to some. 
Woodsyi- WOuld you be able to measure the dimensions of your cubes (esp the inner compartment dimensions). They do look like a nice option, but I can't get over the fact that the inner dimensions of the product link you sent out would not be able to fit an LP!
"Dimensions: 12.8 " H x 13.4 " W x 11.2 " D
Weight: 4.7 Lb.
Compartment Dimensions: 11.2 " H x 11.8 " W x 11.2 " D"