An insert for an earth-boring tool includes a body and a coating disposed over at least a portion of the body. The coating comprises a ceramic comprising boron, aluminum, and magnesium. Polycrystalline diamond compact cutting elements may include a hard polycrystalline material, a supporting substrate, and a coating disposed over at least a portion of the hard polycrystalline material. An earth-boring drill bit may include a bit body and at least one polycrystalline diamond compact cutting element secured to the bit body. The polycrystalline diamond compact cutting element may have a coating comprising a ceramic of boron, aluminum, and magnesium, and may be disposed over at least a portion of a hard polycrystalline material. A method of forming an insert for an earth-boring tool may include forming a protective coating including a ceramic of boron, aluminum, and magnesium over a cutting element.