1 ice cube is not a "m'lo lugmo" (majority of one's mouth), and it is also not the "norm" to eat ice cubes. Some people do this, anyway. For those that do, does it require a bracha? Does it matter if the ice cubes have a flavor, e.g.- frozen raspberry syrup?
A beracha rishona is made on any amount of anything edible (Tur O.C. 210:1), including things which aren't so good (O.C. 204:1). So you would make a shehakol.
Beracha Acharona could depend on a machlokes about shiurim of foods which are normally consumed more slowly. Something which the normal way to consume it is to have less of it at a time, as I assume would be the case with ice cubes (since they are, by definition, freezing cold), is subject to a machlokes if it has a lower shiur. The Taz (O.C. 210:1) assumes that whiskey has a lower shiur because people do not drink it at the normal rate of other drinks, and therefore it's shiur is whatever the standard amount is. The Pri Megadim there cites a number of authorities who argue, among them the Elya Rabba and Magen Avraham.