An identity form: $x_1^3+x_2^3+x_3^3+x_4^3=y_1^3+y_2^3+y_3^3+y_4^3$ I found an identity form: $x_1^3+x_2^3+x_3^3+x_4^3=y_1^3+y_2^3+y_3^3+y_4^3$ as follows:
$$(a+b+c)^3+a^3+b^3+c^3=(a+b)^3+(b+c)^3+(c+a)^3+(6y)^3$$
Where $abc=36y^3$
Poof of this identity is very simple. But the identity nice.

Which reference of the identity? can generalized of the identity?


Equation (shown below) has parametrization:
$(a+b+c)^3+a^3+b^3+c^3=(a+b)^3+(b+c)^3+(c+a)^3+(6y)^3$
$(y,a,b,c)=((8)(3k-4),(256),(24)(3k-4),(3)(3k-4)^2)$
For $k=2$, we get:  $(3,12,64,79)^3=(15,24,67,76)^3$
