I heard while I was watching the history channel that the harder ice gets the less it weighs. So, wouldn't this make the saying that an ice cube weighs the same frozen or melted false?

If you take a 1kg block of ice and let it melt in a completely sealed container it will still weigh 1kg. Ice has a lower density than water to that a cubic meter of water is heaver than a cubic meter of solid ice.

The mass should remain the same but the density of ice is less than water b/c it crystallizes and the molecules spread out. That is why ice floats on water.

To throw the OP a bone,ice does weigh slightly less than water. The thermal energy translates to extra mass in physics.

If you completely seal (vacum seal) the ice. There is a chance that it could wieght the same

But not only have I never heard of anyone saying ice and water weighing the same, the only way to possibly make it happen is not plausible.

When was the last time you needed to vacum seal a ice cibe?

to answer this simply, ice will weigh the same melted as frozen if and ONLY if the total mass remains the same. that means you cant lose any of your mass to evaporation or vaporization. its like taking a pound of lead and a pound of popcorn and comparing them.they both weigh the same... but the lead is more compacted and takes up less space while the popcorn is much less compact and takes up much more volume.