I do it all the time. What you do is find the oldest pair of torn up socks you have that are the same thickness and weight of the socks you want to mend. Same color if possible. Cut out a patch in the shape of the hole, but a good bit bigger, maybe an inch larger all around. Go around the edges of the patch with a running stich, twice, the second time you go around it, put your stitches opposite each other so you have a smooth thread all around the edge.
Sew the patch on the inside of the sock unless its on the bottom of the foot, then sew it on the outside. Use a running stitch and go around it twice the same way you did around the patch. Sew it on first, very close to the edge of the hole. Then sew it again close to the edge of the patch. Same way, running stitch, but you only need to go around once this time.
It sounds complicated but it's really not. It doesn't take very long at all either because most holes are small. If they are very small holes, you can simply hold the hole open and sew stitches close together over the hole to create a "thread fabric". After you do that, then turn the sock and go in a perpendicular direction over the first patch of thread.
I mend things all the time.
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I'm giving it another shot. We will see.
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