Why the expression "a mass of energy" ? I don't think a physics textbook would say something like that. I don't think an energy specifies a mass. I could say "a mass of magnesium" to specify a mass. In Swedish we also have the same tautology (?) "en massa energi" which is a tautology (?) like "a sound of waves" when nothing but a sound could be a wave and nothing but energy could have a mass. So since there is no mass with no energy, why say mass of energy? Energy always has a mass but an energy does not always have a mass (?)
Accompanying the ngrams chart for mass of energy,bundle of energy you will find sets of links to books (from various periods of time) containing those phrases. In the mid-1800s references I glanced at, mass of energy typically refers to a concentration of energy, with energy used in the sense of industriousness, of willingness to work. In the early 1900s, after Einstein's 1905 photoelectric effect article and his mass–energy equivalence article, that usage continues but the term also begins to be used in physics phrases like “The mass of the energy emitted is 0.00084 u” and “At what velocity is the kinetic energy of a particle equal to the rest mass of energy?”.
An energy specifies a mass, or vice versa, via
E=mc². For examples, refer to wikipedia's Mass-energy equivalence article.