Yes, Earth sent processed food to Mars. Vegetables like carrots, cabbage and peppers can be grown with hydroponic techniques which consists in growing them on water. They could also be cultivated in a controlled environment. There are more foods we can eat on Mars like spam, pasta, freeze dried fruit, beef jerky, tortillas and nutella. But for those who like eating nutella with bread it will have to wait because we cant eat bread on Mars. The bread crumbs could cause an accident due to the gravity. Maybe scientists should make crumb free bread. Also soda, liquor, salt and pepper are banned to be eaten in space. There is the option of fertilizing Mars soil but the problem are the gases surround Mars.
Another necessary thing to survive on Mars is water. We can gratefully tell you water could be extracted from martian soil but also could be gained by ice formed by Mars low temperatures or from evaporation.