Given your setup, where you have both Strawberry Perl and Cygwin intermixed, and given that we know you've had problems in the past (
It's Tuesday, so it must be the day for Trouble With Cpan and
Funny-business with Win32 extension module build, as two examples) where Cygwin interferes with your Strawberry setup, I am highly suspicious that now you've got your Strawberry interfering with your Cygwin.
When you're trying to do something in Cygwin -- whether it's installing the module in the Cygwin system perl or trying to run perlbrew to install another perl in Cygwin -- you need to make sure that your paths are all pointing where you think they are, and that they aren't pointing to a conglomeration of Strawberry and Cygwin locations.
echo $PATH
which perl
which cpan
which cpanm
which perlbrew
which gcc
perl -V
gcc -v
At this point, your intial post when asking for help with installing anything should include all that information (or the equivalent with cmd.exe's where or powershell's Get-Command, depending on which environment you are trying to use; I listed the linux-style which this time, since you're currently in the Cygwin environment), because otherwise the monks will waste their time assuming you have a sane setup, and only after half a dozen posts or more will it come out that there's interference between the two yet again.
I am curious why you have both Cygwin and Strawberry. It seems to me that you'd have a lot better luck in your perl module endeavors if you'd just pick one and become fluent in it. If there's a good reason, there's a good reason... but then you should consider figuring out how to keep the two completely separate from each other (make sure that your path in cmd.exe only shows Strawberry and nothing Cygwin, and that your path in Cygwin only shows its options and nothing from Strawberry).
