The authors determine a class of formulae analogous to the Ramanujan formula for the number of representations of a positive integer as a sum of 24 squares. For example the number of representations of \(n-1\) as a sum of 16 squares and 8 triangular number is \[ {1\over 691} \sigma_{11}(n)- {1\over 691} \sigma_{11}\Biggl({n\over 2}\Biggr)+ {690\over 691}\tau(n)+ {42152\over 691} \tau\Biggl({n\over 2}\Biggr)+8192\,\tau\Biggl({n\over 2}\Biggr)+ 25\,\omega(n), \] where \(\tau\) is the Ramanujan tau-function and where \(\omega(n)\) is defined through \[ q^3 \prod^\infty_{n=1} (1- q^n)^8(1- q^{4n})^{16}= \sum^\infty_{n=1} \omega(n)\,q^n. \]