Run next to install apt-cyg on cygwin:

wget raw.github.com/transcode-open/apt-cyg/master/apt-cyg
chmod +x apt-cyg
mv apt-cyg /usr/local/bin

Usage is very similar to Ubuntu's apt-get. E.g. to install mc:

apt-cyg install mc

See also: Use git on cygwin? Add current git branch to your bash prompt in cygwin.

Note: we are not recommending use cygwin anymore once Windows 10 introduced WSL 2. It works much better then cygwin and allows to install you same ubuntu packages as on real Ubuntu! It even supports daemonized applications like Docker in host mode 🥳, Mysqld, Postgres etc...
Just use WSL 2.

#cygwin