Do you record cash when you receive it as revenue if you owe it to someone else?

All companies owe someone somewhere, these are either in the manner of expenses or liabilities.

The question you are posing is too open. Exactly what "cash" did the company receive?

Cash received by a company from sales of goods, services rendered, etc are all recorded as revenue depending on the type of the company.

If the company owes a person money, that debt is recorded as either an expense payable or a liability payable, such as accounts payable.

The company has to record said income on their income statement and then reduce the income as needed for the expenses in reference.