star trek - If the Federation crew was able to beam aboard Borg cubes, why didn't they destroy it from the inside?

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?

Answer

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.