Machines will tell you absolutely nothing about core strength. Especially in that kind of a high rep range.
I don't know how to measure how much core strength you have effectively. You do need good core strength to squat or deadlift heavy though.
Holding a plank is probably the best thing you can do. I would say weighted but I have no idea how you would do that safely.
What is this back machine you speak of?
I don't know what it's called. Basically you get seated as if you are sitting at your computer chair but you are bent over as if you're tieing your shoe or plugging in a cord. And then you sit up, the weight is on the middle of your back and once you reach the upright position you do it again.