Actually, a large nucleus is rarely heavier than the sum of its constituents. If you think about it, this is the equivalent of having a ball stored at the top of a potential energy hill. Once it moves over the edge, the process is all downhill, resulting in liberation of kinetic energy. The heaviest nuclei represent stored-up energy from ``endothermic'' (energy-absorbing) processes that took place in supernova explosions billions of years ago, and are in that sense correctly referred to as ``supernova fossils.'' Anything heavier than iron falls into this category!
Nuclei lighter than iron (57Fe), if they can be regarded as composed of lighter nuclei, are almost always lighter than the sum of their constituents, simply because their binding energy is greater. The process of combining light nuclei to make heavier ones (up to iron) is called nuclear fusion, which also liberates kinetic energy. There are many, many varieties of nuclear fusion reactions, most of which are realized on a large scale in stars, whose main energy source is nuclear fusion. [A nice, romantic aspect of nuclear physics, for a change!] Our own Sun, for example, is one big fusion power plant and has all the pleasant and unpleasant features of the putative man-made versions, such as radiation hazards....
Unfortunately, here on Earth we have not yet succeeded in controlling nuclear fusion well enough to make a reactor that will generate more energy than it takes to run, though billions of dollars have been (and will doubtless continue to be) spent in the attempt. So far all we have achieved with notable success is the uncontrolled thermonuclear reaction [bomb] known as the ``H bomb.'' A nasty feature of thermonuclear bombs is that there doesn't seem to be an upper limit on how big one might make them. The only good thing about them (other than the questionable virtue of ``deterrence'') is that they are not intrinsically as ``dirty'' (in terms of radioactive fallout) as fission bombs, at least not ``per kiloton.'' But I have said rather more than I like about this subject already.