Not only is it important how the ice looks in the glass, it also matters how fast it melts and dilutes your drink. An ice ball has it all - it looks as cool as it is and takes much longer to melt than the ice-cubes.
To make the ice balls, you can use professional ice ball makers of the chosen size. What if you don't have one? You can use water balloons filled with water to the required size and frozen for about 24 hours.