In the paper, we establish some modular relations involving cubic functions which are analogous to Ramanujan's forty identities. We also give new proof of some modular relations of the same nature established earlier by C. Adiga, K. R. Vasuki and N. Bhaskar. Furthermore, we extract interesting partition results from some of our modular relations.

We prove two identities for Ramanujan’s cubic continued fraction and a continued fraction of Ramanujan, which are analogues of Ramanujan’s identities for the Rogers-Ramanujan continued fraction. We further derive Eisenstein series identities associated with Ramanujan’s cubic continued fraction and Ramanujan’s continued fraction of order six.

In this paper, we derive new identities involving a continued fraction of Ramanujan of order twelve that are similar to those of the Ramanujan-Göllnitz-Gordon continued fraction.

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