The Death Star also has a pretty lengthy power-up sequence before it can fire. Good for stationary objects like planets, not stuff that can move at the speeds of a borg cube.
In VOY they established there are limits to how far they can transmit to the collective, and can be "cut off". But it's only under pretty specific circumstances. So if this was in the Alpha Quadrant or the Galactic Core then almost certainly they would be able to transmit the instructions to other Borg. 2nd cube would destroy the Death Star.
Now what's really interesting is if there's a Sith Lord aboard like Darth Vader... He could probably shuttle over to the cube and not be harassed, then mind trick the entire collective (as one)? OR what happens when one gets assimilated, Borg Sith sounds pretty fucking dangerous.
I guess it's also worth considering whether getting vaporized in one shot both A) allows them any time at all in which to analyze, determine an adaptation, and transmit...and B) allows for any meaningful adaptation to be even conceived.
I'm sort of seeing this as the "Dodge this." scene in the Matrix...and honestly, as long as the DS never leaves a survivor, and shoots first, it wins any and every 1v1.
On the other hand, if there is even one extra cube present, I would think its powers of observation would at least let it start working out an adaptation. Also, eventually, the DS, being run by imperials, is going to decide to play with a cube. Try to learn about it, capture it, etc. Once that happens, the odds shift dramatically against it.