Short and Long answer: If your 25-foot cord is made from a stranded heavier duty “lamp cord” that is wired in parallel, then yes, you can cut the cord to fit your project. This type of cord is shown in the image below.
Parallel means that if one bulb is unscrewed from its socket the rest of the bulbs stay on.
One thing to keep in mind though is that Gilbert plugs are made to work with 18 AWG wire with either SPT-1 or SPT-2 insulation. While the SPT-1 gilbert plugs might JUST work with a 25-foot cord, a standard lampstyle cord that requires the ends of the wire be separated, split and installed on terminal screws might be required if you wanted to install a male plug on the wire that is cut off.
Does that make sense? I hope so. In simpler words, gilbert plugs probably won’t work if you mean to make separate cords out of the pieces of the 25-foot cord and you’ll need to choose a different style. An electrician can help with that.
Here is a look at that style of cord:
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And here is one of our favorite Get this Look houses that use wire that can be cut to fit.