I inherited & cashed an IRA from a parent who lived in another state. Do I have to pay taxes on that money in the state my parent lived in or in the state where I reside?

You would not need to file a state tax return for the state the IRA originated from. 

Inheritances are not taxable on a Federal return. 

These are the states that tax their residents on inheritances:

Iowa, Kentucky, Maryland, Nebraska, New Jersey, and Pennsylvania.

Distributions from an IRA, including an inherited IRA are taxed as income in the state in which the recipient resides.

"Inheritances are not taxable on a Federal return. "

 An inherited IRA is a tax-deferred account, and as such is most definitely taxed on the federal tax return.