Infinite families of formulas for sums of integer squares

In 2002, Milne [5, 6] obtained ten infinite families of formulas for the sums of integer squares. Recently, Long and Yang [4] reproved four of these identities using modular forms on various subgroups. In this paper, we prove the remaining six, and show that all of the identities can be proved by interpreting them in terms of modular forms for Gamma(0)(4).