Dropping the cube into the incinerator will reward you with the 'fratricide' achievement.
Fratricide is defined as 'the killing of one's brother or sister'. You could read into this and conclude that the companion cube was secretly your sibling, but it's probably just the developers trying to make you feel bad. It certainly worked on me!
Guide listing help
Unlike normal walkthroughs, in Nice Game Hints you can select just the puzzle you want hints for. Here are listed the puzzles for "Fratricide?" in Portal. The guide you choose only contains information about that puzzle, reducing possible spoilers for other puzzles.
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