If as you say perl -v reports v5.22.1 but cpan is installing to /usr/local/lib/x86_64-linux-gnu/perl/5.20.2/ it looks as though a Ubuntu has done something weird, which wouldn't be unheard of, for example. Do you have a #!/usr/local/bin/perl if so which version? Did you try using cpanm?

My preference, for an easy life, is to install my own version of perl elsewhere, and leave the system one alone. A custom install has resulted in fewer headaches. See also perlbrew.

For over a year, I've started using:
#!/usr/bin/env perl
instead of using direct perl path.
I've read, that env finds an executable from locations in PATH variable, which command also does, but it might resolve to not first encountered path with the named binary, but the best for context, so I've looked @ man which to see what other parameters it has, since env (I didn't find a way for it to just to show the paths, that it resolves), which has -a, that allows to show all possible paths, so I did:
which -a perl
It gave me only one path:
/usr/bin/perl

Forgive my skepticism. You can confirm or refute this easily enough with locate -r /bin/perl$.

You could also say which version of ubuntu you have installed so we can determine which perl is the interloper.

This resolves to:

/snap/core/3604/usr/bin/perl
/snap/core/3748/usr/bin/perl
/snap/core/3887/usr/bin/perl
/usr/bin/perl
[download]

Then I did the following:

for var_p in `locate -r /bin/perl$`; do echo $var_p; $var_p -v| grep '
+(v'; perl -le 'print "-" x 150;'; done
[download]

It gave me the following results:

This is perl 5, version 22, subversion 1 (v5.22.1) built for x86_64-li
+nux-gnu-thread-multi
----------------------------------------------------------------------
+--------------------
/snap/core/3748/usr/bin/perl
This is perl 5, version 22, subversion 1 (v5.22.1) built for x86_64-li
+nux-gnu-thread-multi
----------------------------------------------------------------------
+--------------------
/snap/core/3887/usr/bin/perl
This is perl 5, version 22, subversion 1 (v5.22.1) built for x86_64-li
+nux-gnu-thread-multi
----------------------------------------------------------------------
+--------------------
/usr/bin/perl
This is perl 5, version 22, subversion 1 (v5.22.1) built for x86_64-li
+nux-gnu-thread-multi
----------------------------------------------------------------------
+--------------------
[download]

According to results, all of them have version 5.22.1
then I did: perl -le 'print for @INC;', it gave me:

/etc/perl
/usr/local/lib/x86_64-linux-gnu/perl/5.22.1
/usr/local/share/perl/5.22.1
/usr/lib/x86_64-linux-gnu/perl5/5.22
/usr/share/perl5
/usr/lib/x86_64-linux-gnu/perl/5.22
/usr/share/perl/5.22
/usr/local/lib/site_perl
/usr/lib/x86_64-linux-gnu/perl-base
.
[download]

None of the paths show 5.20.2, so, I don't get it, where cpan gets it from.

I assume you have Ubuntu 16.04.1 LTS; x86_64, was this a new install or an upgrade from a previous Ubuntu version ? If so, what was previous version ?

update Looks like perl v5.20.2 came with Ubuntu 15.04

poj