What is source of the large amounts of energy released in nuclear reactors and in the sun?

Reactors - fission

Sun - fusion

The energy released from fission and fusion is excess nuclear force, also known as residual binding energy.

Binding energy, also known as the strong atomic force, holds quarks together to form protons and neutrons. It is stronger than the electromagnetic force by about a factor of 100, hence it overcomes, in the near scale of the protons and neutrons, the repulsive force between protons and like charged quarks due to the electromagnetic force.

The residual binding energy, then, is what holds protons and neutrons together in the nuclei of atoms. It is somewhat less than binding energy, but it is still more than the electromagnetic force, at least up to a certain distance, so atoms up to lead (AN=82) tend to be stable, and atoms from bismuth (AN=83) and up tend to be unstable.

When we split (fission) heavy atoms, such as uranium, the sum of the nuclear force of the pieces remaining is less than the original nuclear force. Similarly, when we combine (fusion) light atoms, such as hydrogen, the nuclear force of the product is less than the sum of the nuclear force of the component pieces.

The difference in nuclear force is released as energy, in the form of gamma rays and other particles, effectively heat. Its not a large amount of excess energy on the atomic scale, but when you add up the massive number of fission or fusion events that occur, you get a substantial amount of excess energy.

Another way of looking at this is that the end result loses mass. That loss of mass can be compared to the excess energy with Einstein's famous mass-energy equivalence formula e = mc2.

Just to put that into perspective, one kilogram of anything, if completely converted to energy, would be 9 x 1016 joules, or about 21.5 megatons of TNT. The energy released by the bomb at Hiroshima was estimated to be about 13 to 18 kilotons of TNT, from the conversion of only 600 to 860 milligrams of uranium. On the other extreme, the fusion process in the Sun is estimated to convert about 4.26 million metric tons of hydrogen per second into energy, creating 3.846 x 1026 joules per second, or about 9.192 x 1010 megatons of TNT per second.