Short answer (for you that just want to know): No you can’t
A little more info (for those that want it):
I set up a server for a customer DS13_V2 (8 Core, 56 GB RAM)
They tested the server and would like 2 more cores, and then they would be very happy with the power of Azure. That server would replace a 64 Core on-prem server (WOW, that is some power up there in Azure)
I haven’t even thought about just adding CPU or RAM to my Azure servers. Normally it is HDDs, Network, and so on they want.
So I had a look into it, but in the end I had to contact Microsoft Azure Support and ask if it is possible.
They replied within 30 min (10 out of 10 on reply speed), but the answer was not as uplifting. It is not possible to just add a CPU core or more RAM. You will need to upgrade the size of the server. And next level up for us is DS14_V2 (16 cores, 112GB RAM), BUT that would cost us over $600 more pr.month, and we only need 2 more itsy-bitsy CPU cores.
But as MS support said, they also hope the option to add more cores and so on will come to Azure in the near future.
So now I will have to evaluate if 8 Cores are enough, or if we feel the need to spend $600 more pr.month.
BUT I do dig Azure!!