Jeez, you're on a roll today, Madness
By cube conditioning do you mean using the so-called no-chill method of cooling the wort, where the hot wort is transferred to a "cube" or other vessel and allowed to cool naturally before transferring to the fermenter and pitching the yeast?
If so, as I see it there are two reasons you'd do this:
1/ If you didn't have the facility to force cool the full volume of wort, using something like an immersion chiller or plate chiller.
2/ If you wanted to brew a batch but didn't want to (or were unable to) ferment it straight away.
If you're using no-chill you need to adjust the hop additions to avoid excessive bitterness.
Re cold conditioning, it helps yeast to drop out of suspension, so helps with clarity, and also matures the beer. Lagering is a form of cold conditioning. You can cold condition with (i.e. in the fermenter) or without racking, although most would rack.
Then whack the vessel in the fridge and drop its temperature down quickly. If you're lagering a lager, you can leave it for several months to mature.
I do not cold condition. Some swear by it and others reckon it's a waste of time.
So, let the arguments begin!
Oliver