Starting in a pot of cold water, boil the potatoes with the skin on until tender.
While potatoes are boiling, add the sliced cucumber and sliced onions to a bowl and massage with 1 teaspoon salt and set aside.
Once the potatoes are cooked through and tender, peel the skin off. Put the potatoes into a large bowl and mash to your liking.
To the potatoes add olive oil, ½ teaspoon salt, pepper, garlic powder, onion powder, and mix.
Rinse the salt off the sliced cucumber and onion and squeeze the water out. Add them to the potatoes along with the ham and olives. Add the mayo and boiled eggs and stir. Taste for seasoning.