does anyone know how this will effect my cake? Can I continue baking it when it comes back on?
I would not.
Consider that as a business loss.
I would start over, I had that happen to me during a storm. The transformer blew and it was 6 hours before we got power again so there was no hope in saving the cake. A few minutes might not hurt but anything over 10 minutes I would call it a loss and start over.