2 days later, dealer says I owe more money

I saw a similar post to this, but not exactly. I bought a car two days ago. We signed the purchase and sales Dec 30 for a car price of 16,800 (after a $500 downpayment the balance owed was $16,300). The P&S showed we would owe $840 for sales tax, $65 for title search for our trade-in (we lost the title) and $80 for registration. I called before going to pick up the car and asked what the exact amount would be. I was told $16,466.50. I asked over and over if I understood correctly and the figure stayed at $16,466.50. when we went in to finalize the deal and leave with the car, again they told me I needed to pay $16,466.50. I had a bank check from my loan for $16,000 and I paid the remaining $466.50 on my debit card. Two days later (today) the dealer called me and said they made an error and I haven't paid my sales tax yet and I need to pay them. Clearly, the numbers on the purchase and sales do not add up to $16,466.50 but the difference is not the sales tax. The difference is $818.50 not $840.00. Do I have to pay them? I don't have an extra $800 in my pocket and its too late to change the loan.

s. briepp