I don't see a problem actually:
ParametricPlot[{3 t/(1 + t^3), 3 t^2/(1 + t^3)}, {t, -100, 100}, PlotRange -> 4]
However if you do, depending on the version of Mathematica that you didn't specify, you could add an explicit Exclusions option. or cut it in to two pieces and combine:
Show[{
ParametricPlot[{3 t/(1 + t^3), 3 t^2/(1 + t^3)}, {t, -100, -1.01}],
ParametricPlot[{3 t/(1 + t^3), 3 t^2/(1 + t^3)}, {t, -0.99, 100}]
},
PlotRange -> 4
]
Or use a different representation:
ContourPlot[x^3 + y^3 - 3 x y == 0, {x, -3, 3}, {y, -3, 3}]