Many times Federation personnel beamed on board Borg Cubes, so if they were unable to destroy the Borg Cube by their torpedoes and other weapons why not simply plant a high energy destruction bomb from the inside and destroy it.
Secondly, if they were able to beam on board, where are the Borg shields?
There are no explosive weapons aboard the Enterprise that can be transported
Assuming you temporarily disable the transporter's biofilter to allow weapons through, the only physical bomb-like weapons on the Enterprise (NC-1701 D) are antimatter mines and photon torpedoes. Both of these are technically anti-matter, and cannot be transported by NC-1701 D's transporter.
The Federation ship would have to lower its shields to successfully transport, thus opening itself to counter-attack/boarding
Federation transporters typically cannot penetrate deflector shields. In order to transport between vessels, both the host ship and target ship have to lower their shields. (Borg transporters do not have the limitation, FYI).
In Q-Who, the TNG episode that introduces the Borg, the Federation is able to beam aboard because the Borg are busy making repairs to their ship. Typically, Federation crews would be unable to beam aboard Borg ships as if they were close enough to a cube to be within transporter range, as they would be in combat and subject to the limitations above.
Short answer: They do, at least on one occasion
First question: Story telling! Also, the main issue usually isn't just applying damage to a cube. The issue is knowing where to apply it. Also, beaming isn't that easy due to the usual "shields block beaming" issue. There are also explosives and other chemicals shown as being too instable to be beamed, so this might be another reason. As seen in First Contact, the Borg just wiped Starfleet's blockade with obviously minimal or not too serious damages. Once the Enterprise arrives, all they essentially do is coordinating attacks on specific points of the cube (they obviously tried this before, but probably never hit the right spot). Although, to be honest, I'm not sure why this strategically important information wasn't shared/passed along earlier (or it's been ignored? Maybe just more story telling involved...).
Different approach to this question: Why don't they just use beam technology for attacks, like beaming away essential parts of the warp core compartment or anything like that? I.e. you don't have to destroy important things by exploding them, just remove them by beaming?
Second Question: Their shields block beaming just as usual and known throughout the series. However, Borg usually won't waste power on shields unless entering a fight or being engaged. Most often beaming on board a cube happened before fighting, after fighting or while the cube has been damaged. As far as I remember, the only difference is that Borg are able to enter other ships with drones while the shields are still (partially?) intact.
