Forgetting the naturally slower and longer time to cool with a cube in which room temperature would assist in its attempt to cool it down resulting in different temps.

At least I believe a cube sitting in the same temp room as the shaved ice would not be the same temp as the room temperature would take it’s time on heat loss too whilst it sits the prolonged period whereas after the shaved ice melts you take a bite compared to a ice cube and taking a bite after it melts. I dunno.