I'm planning to install Ubuntu 12.04 and setup Sendmail mail server, BIND DNS and Squid proxy server. Will there be any license required from Ubuntu when I download it using apt-get?
What do you mean by "license", user?
If you mean some End User license, some of the programs that you can install will have those.
But in the cases of BIND, Squid, and sendmail don't inherently have any licenses beyond a Free and Open Source Software license, which states that you are free to modify, use, and redistribute the software, and that all modifications and redistribution of the software with those modifications must have the same and/or compatible license.
However, there are no fees to pay, except for the cost of professional support; you can still get community support for free, though. There are also no EULAs that you will need to sign, for the software you are installing.
Licence? Yes, that you are free to modify, use and redistribute all the software, and that the modifications and redistribution have the same/compatible licence. Is called Free and open-source software (FOSS).
Licence? No, you don't need to pay anything, unless you want professional support, otherwise you can obtain support of the community.