How can I install brasero in Ubuntu 16.04?

It's probably repository issue, Your /etc/apt/sources.list doesn't contain what is needed.

sudo echo "deb http://cz.archive.ubuntu.com/ubuntu xenial main universe" >> /etc/apt/sources.list
sudo apt-get update
sudo apt-get install brasero

For more informations You can check this article:
http://packages.ubuntu.com/xenial/brasero

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Edit:

If you're using Ubuntu 18.04 LTS Live CD, you can check the Universe checkbox in "Software & Updates" (second one in screenshot) from the "show applications" menu.