If my opponent casts Lightning Bolt, and I use my Cancel to counter it, does Curse of Echoes still give me a copy of Lightning Bolt, which I could then exile to put 2 +1/+1 counters on Nivmagus Elemental.
Yes. A spell is cast when the process of putting on the stack, making choices for it, and paying for it are complete. Whatever happens to the spell after that doesn't change the fact that it was cast.
Thanks, that's what I thought it was, but I just wanted to be sure.
When your opponent casts Lightning Bolt - Curse of Echoes triggered ability is put onto the stack, then you Cancel the Lightning Bolt - you retain priority and exile your copy of Lightning Bolt using Nivmagus Elemental activated ability. After all this, Nivmagus recieves two +1/+1 counters, your opponent's Lightning Bolt is countered.