Let $$\mathbb {R}$$ R be the set of real numbers, $$(G,+)$$ ( G , + ) be a commutative group and d be a complete ultrametric on G that is invariant (i.e., $$d(x + z, y + z)= d(x, y$$ d ( x + z , y + z ) = d ( x , y ) for $$x, y, z \in G$$ x , y , z ∈ G ). Under some weak natural assumptions on the function $$\gamma :{\mathbb {R}}^2\rightarrow [0,\infty )$$ γ : R 2 → [ 0 , ∞ ) , we study the generalised hyperstability results when $$f:\mathbb {R}\rightarrow G$$ f : R → G satisfy the following radical cubic inequality $$\begin{aligned} d\big (f(\root 3 \of {x^3+y^3}),f(x)+f(y)\big ) \le \gamma (x,y), \quad x,y\in \mathbb {R}{\setminus }\{0\}, \end{aligned}$$ d ( f ( x 3 + y 3 3 ) , f ( x ) + f ( y ) ) ≤ γ ( x , y ) , x , y ∈ R \ { 0 } , with $$x\ne -y$$ x ≠ - y . The method is based on a quite recent fixed point theorem (cf. Brzdęk and Cieplińnski in Nonlinear Anal 74:6861–6867, 2011, Theorem 1) in some functions spaces.