Suspending could be accomplished either by illusion (use of a mirror) or in reality. To do it in reality you'll have to make the the icecube with invisible thread (available at any fabric store) through the middle or by figuring out how to string up the cube after the fact.
Just watch your lighting so as not to reveal the invisible thread.
(I've never done this myself. These are just ideas that came to mind when you presented the problem.)
If you put it on a black surface and a black background, it will appear to be in mid air when you take the photo, for example in this photo. You can't distinguish the background and the surface from each other.
If you really want to suspend it, take a piece of thin black cotton and place it on the ice-cube. Then put some salt on your finger and push the cotton down onto the ice. This will stick it to the cotton so you can dangle it.
you could suspend it with about anything... freeze a string of some sort into the cube and then photograph it... then photoshop the string out of the image.
Think I'll use a black cloth to create the black background.
Suspend the ice cude with a black cotton thread.. Will photoshop the thread out later.
I noticed that when taking the icecude out of the freezer.. the cude is usually "white" in colour (instead of the clear - see through effect we all see from the adverts..)
I tried running it under some cold water... it did put some "clearness" into the cude..
Is there a special process that I should freeze my ice cude in??