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A "cake farm" is a somewhat faster and efficient way to make cake, a sweet but expensive food source. In truth, a cake farm is simply a combination of four smaller farms, each supplying one of the ingredients to a central area with a crafting table, where players can collect the items and craft the cake.
The main sections of the cake farm include a room for crafting and storage, and individual farms for sugar, milk, chicken eggs, and wheat. A very simple and concise design of this is available in a video here.
This method uses pistons to push the canes into water canals which deliver the items into a single collection point. By using this method, replanting sugar canes isn't needed. Example of a simple sugar cane farm can be found there.
If you wish for this to be completely automated, you can use a redstone clock to make the pistons pulse repeatedly. However, this method will get you only one cane at a time in a somewhat inconsistent fashion. So it would be considered more efficient and effective to operate this off a one click lever at the users wish. If you wish to harvest all of the canes simultaneously you can simply wire a button or lever to the pistons.
Once you collected several sugar canes, craft them in a crafting table to make the sugar.
This is a very simple section to do, simply find a cow and use wheat to lure it into your desired section, trap it with fences, and you have a cow which you can infinitely milk. Just right-click the cow with an empty bucket to milk it and you will receive a bucket of milk. You could always set up a chest beside this to store milk buckets, empty buckets and maybe wheat in the case of an accidental escape on the cow's behalf.
Chicken egg farm
A basic egg farm requires chickens. See the design below as an example. Use signs to keep the water from entering the collection area. Put glass around the water and above it, to keep the chickens from suffocating each other in large quantities. There should be a 1 or 2 tall gap above the water for the chickens to breathe in. After this is constructed, eggs can be thrown directly up from the collection area. The chickens will float on the water and their eggs will drop to the floor for easy collection, where they can be thrown back to hatch more chickens. An almost infinite amount of chickens can be contained in the farm with a 100% drop rate. When meat or feathers are needed, a sword can be used to pick off chickens from below.
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Note that after a while, the game may get very slow after use of chicken egg farms. Therefore, it is necessary to occasionally harvest meat and feathers.
An even easier way to do this (even though it takes a long time) is to place a hopper, then get a chicken on the hopper. This gets the chicken stuck. After that, place fences around the hopper to ensure that the chicken does not escape. For even more capacity you can place a chest next to the hopper.
This is simply a case of how much space you wish to dedicate to this section of the cake farm. You could make a small manual farm, or alternatively an automated farm.
Crafting the cake
Have all the farms connect to a room with a couple of chests and a crafting table and you're all set to make hundreds of delicious cakes.