When you [finally!] get the nut off, if the thread on the wiper boss is full of corrosion and crap, don't power brush it or it's tata threads.
I put 4 hacksaw cuts inside a `good' nut, this made it into a cheapo dienut. Cleans the threads up good...

I use a gert big adjustable spanner end-on and use a second spanner to turn the first.

A typical socket is either 6-point (hexagonal) or 12 point (hexagonal in 2 positions). It won't work for an octagonal nut because some of the nut's points will be hitting the "teeth" between the points of the socket. A 12 point socket will work for a square nut, though not a perfect fit. Use a good quality, close fitting fixed open wrench, not an adjusable. Or Vise grips and replace them with hex nuts, assuming the wipers will fit over them. Check first.

You might be able to find a double-square socket - designed for square nuts but with 2 positions like a 12-point socket, though it still would not fit that well because each point wuld have a 90 degree inside angle and you'd want 135 degrees. .

They are often corroded on and the 8 sided nuts are flimsy, can collapse when you apply much torque with a wrench.
I found it easiest to cut 1 corner off the nut, undo with a wrench and then replace with new. Nuts are chromed brass and the wheelbox is soft alloy.

I'm reasonably sure a multiple point type socket will work otherwise a wrench or crescent wrench. Sometimes the nuts are corroded on and require cutting off.

What size socket do I need to remove the 8 sided windshield wiper nuts, and where can I buy an 8 sided socket?