Sunlight has more than one colour
Sunlight looks white, but it contains a range of visible wavelengths. We perceive different parts of that range as different colours. A prism can separate those wavelengths, making the range easier to see.
The sky’s colour involves a different process: scattering.
A small interaction with a big effect
As sunlight passes through the atmosphere, molecules scatter some of it in different directions. For molecules much smaller than visible wavelengths, shorter wavelengths scatter more strongly than longer ones. This is called Rayleigh scattering.
Blue light is scattered more strongly than red light. When you look away from the Sun at a clear daytime sky, some of that scattered light reaches your eyes from across the sky.
Violet wavelengths scatter strongly too. The sunlight reaching us, the atmosphere and our eyes’ sensitivity all help explain why we normally perceive the sky as blue rather than violet.
Why sunsets look different
When the Sun is low, its light travels through more atmosphere before reaching your eyes. More of the shorter-wavelength light is scattered out of the direct path. The remaining direct light can look warmer: yellow, orange or red.
Dust, droplets and other particles also affect what you see. The real sky is more complicated than a single scattering rule.
Never look directly at the Sun. This explanation does not require a solar observation.
Keep wondering
Next time you notice a change in sky colour, think about the path the light has travelled. What might clouds or haze change?