Sorry. Forgot to attach photo.

Maybe spider mites ? Not too sure.

I think it is either aphids or spider mites.

My guess is spider mites. Are there any leaves that have webbing on or under any leaves?

Here are some ideas on how to treat spider mites if it is for sure spider mites:
http://www.gardenguides.com/135781-spider-mites-removal.html

http://www.livingwithbugs.com/spider_mites.html

To keep spider mites away before an infestation is to spray plants with water on the under side of the leaves in the early morning. Spider mites hate water. The only problem is that cucurbits are known to get Powdery Mildew and/or Downey Mildew so watering leaves isn't ideal. But after asking around, spraying in the morning is best because the sun dries out the leaves before PM or DM can usually develop.

If it's spider mites, there will be webbing on and around the leaves. If aphids, a sticky exudate.

My guess from the photo would be aphids.

If you wait for the webbing, you'll have a HUGE mite population.

The secret is to act before the webbing is visible. As in NOW.

Yes there is some webbing that I noticed!!

Can I use baby shampoo solution to spray under the leaves?

Ok so now the black ants have found their way to the cucumber.

I'm guessing they like the honeydew that aphids leave behind right?
So based on the presence of ants, maybe the little bugs I have are aphids?

Or I have both spider mites (webs) and aphids,

This cuke won't last long!

For both aphids and spider mites, first thing to do is wash them off with a good spray of water.

I did, both from a hose then with soapy water made from baby shampoo.

Neither worked and the next day the ants appeared.

Cut off all the affected leaves and throw them in the garbage can. Then start the watering to wash off any remaining bugs and maybe add a bit of soluble fertilizer. The plants will grow new leaves. It's worth a try.