Why is the water from my cold water taps warm?

How warm is warm?

It's very likely that the air temperature is playing a role in the water temperature in your cold water pipes. As your first questioner asked, does the water get colder if you leave the tap on for a little while? If it does, then you know that the water is colder at the source (your well, or the city water supply) than it is after it's been sitting in your pipes for a while.

It's likely that the pipes themselves are not insulated, especially since they are cold water pipes and there's less concern for losing energy (as there is when you're trying to conserve the energy you used to heat the water standing in your hot water pipes). So the pipes and the water resting in them will equalize at the temperature of their surroundings (air) fairly quickly.

The pipes could also be running through an area of wall (or garage or attic) that is uninsulated or underinsulated, or running through open space through joists in your basement or attic, or running through a south-facing wall, or even running through masonry (bricks, concrete), or in contact with masonry, that is directly exposed to the sun. You mentioned warm sunny days and I presume you're in the northern hemisphere. So the sun may be playing a direct role in heating up the pipes. You've noticed how surfaces that receive direct sunlight get a lot warmer (or downright hot, depending) than the surrounding air. The inside of a south-facing wall will be a lot warmer than the inside of a north-facing wall (in the northern hemisphere) when the sun is out in force.

It is also possible that along some length of the pipes, you have hot and cold water pipes touching each other, and your hot water pipes aren't insulated, so that heat is transferred from the hot water pipe to the cold water pipe. If that's the case and you have access to the pipes, you could wrap insulation around the hot water pipe, or at least wedge insulation between the pipes, because you're not only heating up your cold water, you're cooling down your hot water and bumping your hot water bill a little higher.

Whether the pipes are metal (copper, or maybe steel if they're old), or PEX (plastic tubing), the material that the pipes are made of is a good conductor of thermal energy and will not insulate the water in the pipes against gaining or losing energy.

If the cold tap is warm for a while and then cools back to normal, it is a real possibility that you have leak in the hot water line, under the slab. Overnight the hot water leak will beat up the area which includes (usally) the cold water pipe. Depending on where the leak is at, the cold water tap will be cold and then warm when first turned on and then cold again. This is called a slab leak. I have had three. It's almost always the hot line that leaks.