I have a large build that I want to rebuild somewhere else. Is it possible to copy and paste my builds in my own worlds? If so, how do I do it? 

Info possibly needed:

server type- private

device- Lenovo ThinkPad Yoga 11e

build size- 14x25x16

If it is on the same server it is possible,

You do /copy and it makes you choose two blocks and anything in the cube of blocks will be copied. Then you can do /paste (in any world in the server) and it will paste.

1 hour ago, Matthew132 said:

If it is on the same server it is possible,

You do /copy and it makes you choose two blocks and anything in the cube of blocks will be copied. Then you can do /paste (in any world in the server) and it will paste.

It's not letting me use the command. It's saying "/client: Unrecognized command: 'copy'." What should I do now?

If you are a server owner you can put your files into /extra/import/ folder and use /import to import your local worlds.

It's a lot easier for people to answer accurately if you don't use confusing and misleading terms. What you're calling a "private server" is just singleplayer mode.
Unfortunately there is no way to copy and paste builds in singleplayer. However, you can run an actual private server, such as MCGalaxy, and then import your save map, and use its /copy and /paste commands to work on your map there.
Read "README.md" to set it up. Then, save your singleplayer world, and put it into the extras/import folder. Then, use /import [levelname]
Then you may use /goto [levelname] to get to it.

20 hours ago, King_Kinma said:

It's not letting me use the command. It's saying "/client: Unrecognized command: 'copy'." What should I do now?

In that case your using a single player world not a server. Sadly from what I know of there is no way to /copy and /paste without going into your game files. I suggest just going into a server as it gives you more building options. If not you could go with Goodly's solution.