The authors construct theta function identities that enable them to express certain theta functions in the form \(\eta^d(\tau)F(P, Q, R)\), where \(\eta(\tau)\) is the Dedekind eta function, and \(F(P, Q, R)\) is a polynomial in Ramanujan's Eisenstein series \(P\), \(Q\), \(R\). The powers treated are \(d= 2,4,6,8,10,14\), and \(26\), these being the even powers of \(\eta(\tau)\) that are lacunary. The paper generalizes results of Ramanujan for \(d= 1\) and \(d= 3\). Identities derived for \(d= 26\) lead to a new expression for \(\eta^{26}(\tau)\). A new representation is also obtained for Ramanujan's function \(\tau(n)\), generated by the 24th power of \(\eta(\tau)\).