I am trying to learn what this small blue cupboard on the left side of the table is called? It's a corner cupboard but I am not sure what the technical term is:
I am not certain what you mean by a "technical term" for it. I would call it a corner hutch or a corner display hutch or maybe a corner bookcase.
Why corner? Because it is shaped to fit in a corner.
Why hutch? A hutch is sometimes something that sits on top of a bureau, table, desk, or other piece of flat-topped furniture. However, hutches can also be a free-standing shelved storage units with doors. The impression people have of "hutch" will vary by region.
Why bookcase? It's got books on it.
I can tell you also that I would not call it