Atoms are closer in FCC. Does it imply high bond strength?
It does imply low bond energy.
Not necessarily. In general, materials with FCC or HCP have a high ionic or metallic character, since they are close packed. That is, since ionic and metallic bonding is isotropic in nature, the atoms don't care as much about relative orientation and just fill space the most efficiently as possible.
Also, I think you may have confused the fact that surfaces with high packing densities generally have a lower surface energy. This is not the same as bonding energy.
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