Parametric Equations for Three Series of "Quadruples" for the Formula A^3 = B^3 + C^3 + D^3

This paper is a supplement to the previous work “On the First Series of “Quadruples”of Numbers by Analogy with Pythagorean “Triples” for the Formula A^3 = B^3 +C^3 +D^3”(April 8, 2026). Here we present explicit parametric formulas for three infinite familiesof integer solutions to A^3 = B^3 + C^3 + D^3 with A = B + 1, which were originally givenin tabular form. For each family we derive closed-form expressions and list the first 20numerical examples.