The contributions of the high-order terms in virial equation are approximately incorporated into the truncated virial equations with three terms in this paper.By means of the approximate expression of second virial coefficient and some transformations and extensions of truncated virial equations with two and three terms，the general cubic equations of state proposed by Martin and Abott，and some quasi-empirical equations of state or their similar forms are derived approximately，such as van der Waals，Clausius，Redlich-Kwong，Usdin-McAuliffe (Fuller)，Martin，Peng-Robinson，Patel-Teja，Harmens-Knapp，Tong-Liu，LHSS，Modified Kumar-Starling，Du-Guo，CCOR，SIRK，Lee-Edmister equation，etc.The results indicate that the above equations are supported by statistical mechanics in some way.Besides，nine new cubic equations of state are obtained with the same method，some of which are flexible in form or parameters and prospective in application.