Yes, you can pay cash for any property you want to buy. Cash is preferred.
Just keep in mind in today's market just because a home is listed for $70,000 does not mean you can get it for $70,000. There may be a bidding war.
I do highly recommend that you hire a Realtor with experience in today's market. You need a strategic agent that can make you a winner in real estate.
The LIST PRICE doesn't always mean that that will be the SELLING PRICE; sometimes they will List LOW to attract multiple offers.
Talk to your Realtor about doing a CMA to find the Market Value; maybe 70 is realistic, maybe not.
Don't forget that you will have Closing Costs' anywhere from $3000 to $6000 would be a guess.
You should Inspections, at least General and Pest, maybe more; add another $500 or so.
Good luck and may God bless