Why cannot I chmod in Cygwin on Windows 8 CP?

I can't chmod group permission in Cygwin on Windows 8 so that I can't ssh connect to a server using an ssh key.

Bash prompt warning: "Permissions 0660 for '/home/KeepZero/.ssh/id_rsa' are too open. It is required that your private key files are NOT accessible by others."

KeepZero@t400win8 ~
$ ls
test

KeepZero@t400win8 ~
$ ls -l
total 0
-rwxrwx--- 1 KeepZero KeepZero 0 Mar  4 15:07 test

KeepZero@t400win8 ~
$ chmod 700 test

KeepZero@t400win8 ~
$ ls -l test
-rwxrwx--- 1 KeepZero KeepZero 0 Mar  4 15:07 test

KeepZero@t400win8 ~
$ chmod 777 test

KeepZero@t400win8 ~
$ ls -l test
-rwxrwxrwx 1 KeepZero KeepZero 0 Mar  4 15:07 test