Review of Information Engineering and Applications 2412-3676 2409-6539 10.18488/journal.79/2014.1.2/79.2.93.101 Review of Information Engineering and Applications On Homogeneous Cubic Equation with Fourunknowns x3+y3= 2lzw2 Review of Information Engineering and Applications Review of Information Engineering and Applications 12-2014 2014 12-2014 12-2014 1 2 93 101 30 Nov 30 Nov The homogeneous cubic equation with four unknowns represented by the Diophantine    equation  x³+y³= 2lzw²   is analyzed for its patterns of non – zero distinct integer solutions. A few interesting properties between the solutions and special numbers, namely, Polygonal number, Pyramidal number, Centered polygonal number, Stella octangular number and Octahedral number    are presented.