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Given that Storm Trooper rifles are the most basic-ass laser weapons imaginable and don't even consistently kill a person wearing physical armour, let alone a shield, this battle is over basically the minute the Borg beam over to the Death Star. The cube will be destroyed by the main D.S. gun, but it takes so long to aim and charge that half the station would already be assimilated - or at very least full of laser-immune Borg.
Additional thought: 70%-ish of a Borg cube needs to be destroyed before its distributed system collapses. If the D.S. main gun is too powerful it may just shoot straight through and leave the Cube with enough intact to keep going at least one more shot.
The 2nd death star shoots a cruiser out of the sky in ROTJ so they get at least 1 of the 20,000 borg cubes
They can dial in the power of the death Star shots to match the target.