On the First Series of "Quadruples" of Numbers by Analogy with Pythagorean "Triples" for the Formula A^3 = B^3 + C^3 + D^3

AnnotationThis paper presents the first four parametric families of integer solutions to the Diophantineequation A^3 = B^3 + C^3 + D^3 (and, in one case, to A^3 = B^3 + C^3 + D^3 + E^3). The series areconstructed using a specific integer sequence 1, 4, 10, 19, 31, 46, 85, . . . (obtained by summingconsecutive triangular numbers) and elementary arithmetic operations. For each series, explicitexpressions for A,B,C,D (and E) are given through parameters, and numerical tables up to50 members are provided. The work is a translation of the original Russian article published inthe periodical “Academy of Trinitarism”. Full Russian text with detailed tables is available atthe reference below.Original publication:Э. И. Хельмдах, “О первых рядах «четверок» чисел по аналогии с Пифагорейскими «трой-ками» для формулы вида A3 = B3+C3+D3” // “Академия Тринитаризма”, M., Эл No. 77-6567, публ. 29515, Май 28, 2025.URL: (https://www.trinitas.ru/rus/doc/0016/001k/00165869.htm)