The depicted shape of subatomic particles I physics books and such, I understand why they show atoms as spheres because they have the electron cloud. But why are protons, neutrons, and electrons spheres? I guess people say that because of calculations in nuclear physics, they turn out to be a sphere, but why naturally. Also, are quarks and neutrinos also spheres it are they string-like things?
 A: What about the colours in the pictures?
As the  poet says
"Protons are Red,
Electrons are Blue,
Neutrons are Grey,
And so are You"
Colours and shapes  are just artist's illustrations. Pictures  don't mean anything. If they used a dot it would be too small to   see it; if they used a cube it would be misleading so what else can you use?
Elementary particles don't have shapes or colours. They just have scattering cross sections.
A: By machine-gunning protons with electron bullets, you can look at the angles at which the electrons bounce off them and determine something called a structure function for the proton. If there are no preferred directions for the electrons to bounce off in, then you are justified in modelling a proton as an object with a finite diameter, which is radially symmetric- in other words, sphere-like. This is why protons and neutrons are commonly represented as little three-dimensional spheres.
But if your bullets (electrons) carry enough punch, then they can penetrate those little spheres (protons or neutrons) and reveal whether or not there are smaller things (quarks) running around inside them. You then get a structure function that no longer represents a featureless sphere because the bullets are now blasting their way inside and bouncing off the internal parts of the sphere which are not uniformly distributed inside it.
So for low-energy electron bullets, a proton is a tiny sphere but for high-energy electrons it is a complicated thing with internal constituents.
When you shoot electron bullets at other electron bullets, to the limits of the precision of the experiment the electrons reveal no internal structure and behave as if they were not tiny spheres with finite (but tiny) diameters but instead infinitesimal points of essentially zero size. Likewise for neutrinos.
