Can I apply Cina visa and Hong Kong visa at the same time by showing the invitation letters from China government?

You can only apply for China business visa by using invitation letter from Govt of china along with company invitation letter from china. You can't get Hong Kong visa by using them because Mainland China and Hong Kong apply different visa rules. You have to get a proof of the proposed business visit to Hong Kong, e.g. letter issued by your employing company to confirm your proposed business activities in Hong Kong, invitation letter issued by a local company, letter issued by a trade body to confirm your attendance at trade fairs and exhibitions, etc.