Yeah, I won't think it can be done from Cpanel.
So basically you want anantshri.com parked on anantshri.info and again the subdomain blog.anantshri.com to be parked on blog.anantshri.info. right?
This will need to be done manually in the apache configuration file. Or you should use htaccess rules instead of parked domain. Unpark .com from .info and htaccess rules for redirection.
Dont create the subdomain "blog.anantshri.info" under the domain "anantshri.info", Go to WHM and create a new account with "blog.anantshri.info" and under that you can try adding "blog.anantshri.com" as park domain which should work fine. Also note, make sure you create seperate Cpanel accounts from your whm with these domains "anantshri.info" and "anantshri.com", so that WHM can generate your Zone entries for subdomains like "blog."