I have a 200 amp panal in a new basement less then 5yrs old. Square D box.
There is about 8 open spaces left. There is a dryer,oven/cook top,60 amp sub panal,
And lots of 20 and 15 amp breakers. How do I figure if there is room in this box for another sub panal for the basement finish? When adding up the breakers now there is a total of 565 amps total now.
Thanks for the help.

The question is not do you have room for a sub-panel. A sub-panel does not draw anything. And you could fill it with 20A breakers that each feed one amp loads.

The question is does your service have enough capacity for the basement re-model. A demand load calculation is the only way to tell this.

Counting up the breaker is a meaningless number. It's like counting up the numbers on your car's speedometer.

I will say, your 200A service will most likely be fine if you have that many open spaces still.
What could you possibly add to a basement finish? 3-4 new circuits?