On the First Series of "Quadruples" of Numbers by Analogy with Pythagorean "Triples" for the Formula A³ = B³ + C³ + D³

AnnotationThis paper presents the first four parametric families of integer solutions to the Diophantineequation A³ = B³ + C³ + D³ (and, in one case, to A³ = B³ + C³ + D³ + E³). 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)