Ah, so you agree that the energy transfer doesn't differ. Good. You said earlier that it did, which had me confused.
So, yeah, at point in time t, when the fluid being cooled has experienced delta T, the amount of energy pulled from it is the same, regardless of how long it took to get to delta T. Good, that's what I was saying. The heat energy went into the ice, either warming it, melting it, or warming the melted water. We know it didn't go into the glass or atmosphere, that would violate one of the LAWS of thermodynamics.
So, knowing that all of that heat energy went into the ice, all we have to do is decide how it was distributed. If any of the solid ice remain un-heated (from -10 to 0C), then the balance of the energy must have been removed by phase change or heating the water.
So, does one large sphere warm more evenly than 4 small cubes? I don't need a precise answer, just >, <, or =. Or is it sometimes yes, sometimes no, depending???