Boiling water transfers energy to an ice cube this is an example of?

I'd say thermal energy. I say that because if I remember correctly the Second law of thermodynamics describes the energy in this case the boiling water (heat) to areas that are not hot like the ice cube. With heat energy we deal with warm moving to the an area of cold. The molecules in the ice cube from what I remember in college  aren't moving at all hence the block of ice but when heat is added to the ice cube then the molecules in the ice cube start moving and getting excited, which causes the ice cube to start melting, as my bio teacher in college said.

Hopefully this helped and good luck.

No they’ve not done that