Even with a cash offer there are closing costs. Those costs are much lower than the closing costs on a home loan. When a home is being financed sometimes buyers will ask for cash back from the sellers to cover closing costs.
Before making a cash offer find out what the closing costs will be and adjust your offer as needed. If you will need more cash than you have for a full-priced offer and closing costs, offer less than the full price. It is really pretty simple. I often ask a title company for help calculating closing costs on a cash sale.
Instead of a pre-approval letter for a loan a cash buyer needs to provide proof of funds, like a bank statement.
Cash offers are more common than they used to be. Last Fall about 31% of purchases were cash.