hi,
virtuoso tells you these values. just simulate and print or annotate the component parameters of the transistor you want. a lot of parameters will be listed and you can search for the related capacitances. I guess, the input capacitance of an inverter is Cnmos + Cpmos. Cnmos = Cox,n + Cgd,n + Cdb,n + Cgs,n. Cpmos is the same as nmos.
Virtuoso can provide you with these values, but if you want to calculate them by hand, it is a complicated process and it doesn't promise an accurate result.
This book explains the capacitance issues very well in one of the first chapters: CMOS Digital Integrated Circuits Analysis & Design by Sung-Mo (Steve) Kang and Yusuf Leblebici