Would an electron have to absorb or release energy to jump from the second energy level to the third level?

Electrons are attracted to the nucleus of the atom of which they are a part; this is because of the electrostatic force between the negatively charged electron and the positively charged nucleus. Therefore it takes energy in order to pull an electron farther away from the nucleus and to enable it to remain at a greater distance. This is exactly the same phenomenon as raising a heavy object such as, let us say, a Bowling ball, to a greater elevation. It takes energy to do it, since you have to overcome the force of gravity.