The number of representations of a number by various forms

In a recent paper, I began with four classical results due to Jacobi, Dirichlet and Lorenz which give the number of representations of a number by various forms involving squares in terms of divisor functions. I deduced another sixteen similar representation theorems involving triangular numbers and/or squares, including celebrated results of Legendre and Ramanujan (and omitted a seventeenth, given here). In this paper I deduce a further twenty–nine representation theorems involving triangular numbers, squares, pentagonal numbers and octagonal numbers.