Now that summer has come, ants are coming out and they're very annoying. When I lifted my cucumber plants up earlier, there were so many ants. There were also many winged ants. I am sure there's a nest in the soil because every time I dig up the soil in that area, ants come swarming out of the hole. Is there any solution to kill off or at least control them? I tried making a liquid solution with four parts sugar, one part Borax, and some water, but the ants haven't even touched it since I placed it in the garden bed. The pictures don't really show the ants that well but they're definitely there.

If the ants are in an area without plants, you can keep stirring the soil up. If in areas with plants, you could pour Insecticidal Soap into the mounds.

It is a possibility what you are calling winged ants are instead termites. They take to the air in mating flights this time of the year. Ants do this, too. Terro makes a product that is a liquid bait in a stake that you push into the ground. I've used these with good results.