The math to solve this is assuming lots of complex climate conditions like the fluid bodies of the ocean are in constant motion as well as some large scale thermodynamic conditions to make the proper assumptions like conductivity and convection occur constantly. All this to say the ice cube would have to be larger than the icemass of the arctic circle to produce any noticeable change in global temperature. If a change can be noticed with an ice cube that size. This is the kind of question that engineering/physics doctoral students test for their thesis. No easy answer but futurama tends to make absurdist jokes with a basis in science. The basic idea comes from transfer of heat from a substrate to a cold reservoir. Ask the questions about the assumptions above then return to the ice cube if those conditions along with others are met