Many of european countries offer free education (almost free - there might be some minimal fees that you have to pay. You need to cover your living costs). Students are included under free education.
If you want to study in Europe, your parent's income may not be the deciding factor in the quality of education you receive. There are world class tuition free universities (for international students as well) in European countries such as Norway, Sweden, Germany, Italy, Finland. You might have to give administrative fees of few hundred Euros. If you are planning to study abroad this might be your cheapest option to get a cheapest degree from top universities in Europe.
Note: Living costs/Health insurance etc are not covered (You can still get scholarships based on availability but there is close to zero tuition fee!).