Cdtjkyj

Im very new to making latex so all the tutorials I have found about my question were too hard to understand or didn't do exactly what I wanted.

I already have the graph I want without the coloring:

begin{figure}

centering

begin{tikzpicture}

      draw[->] (-2,0) -- (2,0) node[right] {$x$};

      draw[->] (0,-2) -- (0,2) node[above] {$y$};

     draw[scale=0.4,domain=-1.71:1.71,smooth,variable=x,black] plot ({x},{(x)^3});



      end{tikzpicture}

end{figure}

A tricky way:

documentclass[tikz,margin=3mm]{standalone}

begin{document}

begin{tikzpicture}

fill[blue!20] (-2,-2) rectangle (2,2);

fill[green!50] (0,0)--({-1.71*0.4},{0.4*(-1.71^3)})--(2,-2)--(2,0)--cycle;

fill[green!50] (0,0)--({1.71*0.4},{0.4*(1.71^3)})--(-2,2)--(-2,0)--cycle;

draw[->] (-2,0) -- (2,0) node[right] {$x$};

draw[->] (0,-2) -- (0,2) node[above] {$y$};

draw[scale=0.4,domain=-1.71:1.71,smooth,variable=x,black,fill=green!50] plot ({x},{(x)^3});

end{tikzpicture}

end{document}

Here is my suggestion, without slightly line, because the filling is made differently (code modified from AndréC answer):

documentclass[tikz,border=5mm]{standalone}

begin{document}

begin{tikzpicture}



begin{scope}

    clip[postaction={fill=green!50}] (-2,-2) rectangle (2,2);

    fill[scale=0.4,domain=0:5,smooth,variable=x,blue!20] plot ({x},{(x)^3}) |-(0,0);

    fill[scale=0.4,domain=0:-5,smooth,variable=x,blue!20] plot ({x},{(x)^3}) |-(0,0);

    draw[scale=0.4,domain=-1.71:1.71,smooth,variable=x,black] plot ({x},{(x)^3});

end{scope}



draw[->] (-2,0) -- (2,0) node[right] {$x$};

draw[->] (0,-2) -- (0,2) node[above] {$y$};

end{tikzpicture}

end{document}

(Code edited with marmot's useful suggestion: using postaction to reduce redundant code.)

With pgfplots, this is easy to do.

Here is a pure tikz DIY without a single piece of pgfplots!

documentclass[tikz,border=5mm]{standalone}



 begin{document}



begin{tikzpicture}

fill[blue!20] (-2,-2)rectangle(2,2);

begin{scope}[transparency group,opacity=.9]   

fill[scale=0.4,domain=0:1.71,smooth,variable=x,green] plot ({x},{(x)^3})coordinate(a)|-(0,0)node[midway](m){};

fill[green](a)--(2,2)|-(m.center);

fill[scale=0.4,domain=0:-1.71,smooth,variable=x,green] plot ({x},{(x)^3})coordinate(b)|-(0,0)node[midway](n){};

fill[green](b)--(-2,-2)|-(n.center);

end{scope}

draw[scale=0.4,domain=-1.71:1.71,smooth,variable=x,black] plot ({x},{(x)^3});

draw[->] (-2,0) -- (2,0) node[right] {$x$};

draw[->] (0,-2) -- (0,2) node[above] {$y$};

end{tikzpicture}

end{document}