The following table has the inputs, $x,$ and the outputs for two functions, $f$ and $g.$ Use third differences to determine whether a cubic function exactly fits the data with input $x$ and output $f(x).$

$\backslash$table$[[x,0,1,2,3,4,5],[f(x),0,2,8,30,71,127],[g(x),0,0\mathrm{.}4,2\mathrm{.}8,9\mathrm{.}2,21\mathrm{.}6,42]]$

Complete the table below to find the third differences.

$\backslash$table$[[$Outputs$,0,2,8,30,71,127],[$First Differences,$2,,22,56,,],[$Second Differences,$4,,19,,,],[$Third Differences,,,,,,$]]$

$($Type integers or decimals.$)$