Yes, everything takes up space.
Cubes
No. Water expands when it freezes so when it melts, it will take up a smaller volume.
A person would be able to purchase light up ice cubes at walmart, amazon, or many of the major retail companies in the world. A popular brand is "Lited Ice Cubes"
because water heats up faster
Yes. Salt, for example, will speed up the melting of ice cubes.
a ice cube melts when it heats up
Ice does float, but if you put in multiple ice cubes, the ice cubes underneath can't push up over and on top, so it looks like they're floating in the middle of the glass.
Ice cubes explode in a drink because they are melting at a fast rate. The ice cannot contract fast enough to keep up with the melting, which causes it to crack.
Snow/ice packed into tight "cubes"
No, but it will take up slightly less space after melting.
Water is a special substance that expands when solidified.
An example of a cube that can hold liquid is an ice tray. An ice tray is made up of several cubes. Water is poured into these cubes then frozen to help cool drinks.