Wash the potatoes thoroughly and peel them.
Cut the potatoes into appropriate-sized pieces.
Put the potatoes and water into a pot and boil until cooked.
Mash the potatoes and season with salt and pepper.
Thinly slice cucumber, carrot, and onion, then remove excess moisture.
Add the sliced vegetables and mayonnaise to the mashed potatoes and mix well.
Add a little sugar to taste, if desired.
Place the finished potato salad in a bowl.