I think most of your reasoning is fine. What I'm not sure about is your opinion that "sugar is the most important word when talking about the substance called sugar cube." I think what word is the most important one depends. Your example with the kid is a good one, because when you're that young it may be more important to learn the word sugar than cube. But if you were to present a sugar cube to an older kid, who is already familiar with the word and substance sugar, and who is presently learning words of different shapes, he'd probably answer "cube" rather than "sugar."What's the incorrect point of my thought above? Or why am I wrong? Or where in my thought above did I make mistakes?
I think you have to say "cubed sugar" and not "cube sugar".You say cube sugar when you want to contrast it to granulated sugar, eg 'Can you pick up some sugar please? Not loose sugar but cube sugar.' 'I put out some cube sugar for the guests coming' (implicit contrast).
Otherwise, 'sugar cube' would be more common.