「自由クラス理論」非標準集合論コミュの Taxicab Number

Identity :

I made one of the identity of TaxiCab Number as follows
(1679616*a^16-66096*a^10*b^6+153*a^4*b^12)^3 + (1679616*a^15*b+279936*a^12*b^4-11664*a^9*b^7-648*a^6*b^10+9*a^3*b^13+b^16)^3 = (1679616*a^16+559872*a^13*b^3+27216*a^10*b^6-3888*a^7*b^9-63*a^4*b^12+3*a*b^15)^3 + b^48
Some examples :

11585457155467377217,1,1,
1508575574198742937512498370075033,2,1,
392161712977726219126916526583291247563177,3,1,
381314174837561337012118665045281362401428092609,4,1,
16969197132907710102386910645228741045813775110144001,5,1,

Where the triplets represent Sum of two cubes, a, b
I want to know known all identity of TaxiCab Number
If you know the other identity then tell me it
I know Ramanujan's identity
(x^2+7*x*y-9*y^2)^3 + (2*x^2-4*x*y+12*y^2)^3 = (2*x^2*+10*y^2)^3 + (x^2-9*x*y-y^2)^3