There's a hard cap on population equal to the planet class.  Can you try terraforming another tile to raise the class and see if your cap goes up?

Is this your capital planet.

could you post a screenshot of the colony where it is not working?  

so it wasn't next to a city?    They don't provide +2 pop cap, they provide +2 population adjacency (which is +20% pop cap for carbon cities, +0.2 flat for silicon cities).  I figured that was the misunderstanding, hence wanting a screen shot.

glad I could help, even indirectly

your colony capital is not a population building.  It is an All Construction building.  You are getting a 15% bonus to food production now, but 0 food is 0 food.  There are no population enhancements next to your Food Distribution.  It is working just as intended.

Ok I will admit I'm silicon, so I'm not familiar with these buildings, but these buildings dont affect population caps, but cities do. These buildings affect how much food you have. Look at the top of  the screen on your main screen. You use food to build cities on any planet.

OK, so exactly what do I put Food Distribution or Hydroponic Farms next to in order to achieve the increase in population cap? Do I only get the population cap increase if they're next to a city?

There is a planetary resource which will increase pop cap as well .. it'll give a +2 cap to the planet when first mined.  But other than that, Publius is 100% correct.

The main reason for Food Distribution is to increase food production.  The +2 adjacency to cities is nice, and I will occasionally use them just for that, even if the food increase is minimal (especially when there are already 2 cities on the planet, and I'm low on food) but they are not in-and-of-themselves pop cap boosters.