So you want a function f(x,y) such that f(107300, 212000)= 19, f(267500, 11700)= 79, etc.? (You seem to have droped a y value for the last one.)
Since you have 8 values, you can set up 8 equations and solve for 8 coefficients. I would try something like
[/tex]f(x,y)= A+ Bx+ Cy+ Dx^2+ Exy+ Fy^2+ Gx^3+ Hy^3[/tex]
Now putting those values in for x, y, and f(x,y) gives you 8 linear equations to solve for A, B, C, D, E, F, G, H.
(To have a general cubic in two variables,we should also include and but that would require two more data points. The "resticted" cubic given will fit those 8 points for some coefficients.)