I have a Common stock authorized of 5,000,000, 1 par
And a commons stock issued for cash of 3,000,000, $10 per share,
I am trying to figure out the retained earnings, will I be subtracting the cash stock from the authorized amount and then multiply that by the $10 per share?

Retained earnings in the Balance
Sheet has nothing to do with what you are talking about.
Retained earnings are the earnings of the business that emanates from the Income statement.
This is the accumulation of the profits of previous years, not forgetting that dividends are paid from retained earnings.