The color-charged quarks of one proton "glue" themselves to the color-charged quarks of another proton, even though the protons are color neutral.
What holds the nucleus together?
The strong force only binds quarks together
Protons and neutrons are color-neutral objects,
but, are made of several color-charged quarks.
The color-charged quarks of one proton
"glue" themselves to the color-charged quarks of
another proton, even though the protons are color neutral.
This residual strong
interaction is strong enough to overcome the electromagnetic
repulsion between protons. 
THIS IS WHAT BINDS THE NUCLEUS!
