Two ice cubes are pressed over each other to form one cube. Which force is responsible for holding them together?

 Ice is a solid state of water. In ice every water molecule is associated with four other water molecules. It has an open cage like structure.
Complete answer:
Intermolecular force is the force of attraction that held the molecule together. There are various types of intermolecular forces like Van der Waals force, hydrogen bond, covalent attraction, ionic interaction etc. The type of intermolecular forces depends on the type of molecules.
Van der Waals force is weak intermolecular force which exhibit between two non polar molecules
Hydrogen bonding is the electrostatic force of attraction that binds the H-atom of one molecule with electronegative atoms of other molecules of the same substance.
Covalent compounds exhibit covalent force of attraction.
Ionic molecules are held together by an electrostatic force of attraction known as ionic force. There is ionic interaction between oppositely charged ions.
In ice every water molecule is associated with four other water molecules by hydrogen bonding in a tetrahedral fashion. Due to hydrogen bond formation ice has an open cage structure with a large empty space.
 

When two ice cubes are pressed together the water molecules present on the surface of the two cubes form hydrogen bonds with each other and so two cubes unite to form one cube.