Can't make new dir with mkdir

Probably a parent directory in the path does not exist.

You can try with

mkdir -p /path-to-directory/directory-name

See man mkdir

   -p, --parents
          no error if existing, make parent directories as needed

---

If you get a permission denied error, you have not permissions to create a directory in the specified path.

Check if you can get around the problem by modifying the group membership or ownership, so that you get the permission needed for the whole directory path involved.

Otherwise you need elevated permissions, so try with sudo

sudo mkdir -p /path-to-directory/directory-name

sudodus's answer appropriately addresses how to create all directories along the given path. Alternative way would be via Python. This is especially useful if you're developing software for Ubuntu in Python and need such functionality. Calling mkdir as external command would add overhead of additional process and extra forking which would waste resources. Luckily Python's standard library, specifically os module has makedirs() function:

$ python3 -c 'import os,sys;os.makedirs(sys.argv[1])' test_1/test2/test_3
$ tree test_1
test_1
└── test2
    └── test_3

2 directories, 0 files

Note that such behavior also can be achieved in Perl, which is another scripting language that comes by default with Ubuntu.