Cucumbers are nutritious and good for you both with the skin and without the skin of the Cucumber.
But you really should eat the skin of the cucumber too since the skin of the cucumber contains even more nutrition than just the cucumber itself.
When you peel off the skin of the cucumber you remove a good amount of fiber, as well as certain vitamins and minerals that benefit your health.
So for the health benefits eat the skin along with the cucumber because otherwise you're not getting the most out of the cucumbers.