On the OCTIC Equation with Six Unknowns 4(x6−y6) − (x2−y2)(x4+y4+10x2y2) = (z4−w4) p2−4T4p2(x2−y2)

We obtain infinitely many non-zero integer sextuples (x, y, z, w, p, T) satisfying the non-homogeneous equation of degree eight with six unknowns given by 4(x⁶−y⁶) − (x²−y²)(x⁴+y⁴+10x²y²) = (z⁴−w⁴) p²−4T⁴p²(x²−y²). Various interesting relations between the solutions and special numbers, namely, polygonal numbers, Star numbers, Stella Octangular numbers, Pronic number, Jacobsthal number, Jacobsthal-Lucas number, keynea number are exhibited.