ContourPlot[(1-x^2-y^2)^3-27x^2*y^2==0,{x,-1.2,1.2},{y,-1.2,1.2}]

ParametricPlot[{(Cos[t])^3,(Sin[t])^3},{t,0,2Pi}]

Simplify[(1-x^2-y^2)^3-27x^2*y^2/.{x-> (Cos[t])^3, y-> (Sin[t])^3}]