Latent heat of fusion is the amount of energy required to raise a material by 1 degree given that there is 1 kg of the given mass. Let’s assume that the mass is measured after it has been taken out and the temperature change is measured using an ideal thermometer. The only variable left in the experiment is the energy as we cannot always guarantee that all of the energy goes in to melting the cube (it could be dissipated in to air etc). So the answer is always less as realistically, the energy (or power) we’re putting in to the ice cube is dissipated elsewhere in some form.