Find the max and min values of function with using Lagrange multipliers

Question

$\mathbf{f(x,y,z)=x^3+y^3+z^3}$ constraint to x+y+z=4 find max and min values of function. Oh k. I find λ as 16/3. $\mathbf{∇f=(3x^2 , 3y^2 , 3z^2)}$ and ∇g= as (1,1,1) so $3x^2$ must be equal to λ so $x= \sqrt{λ/3}$ and I typed at constraint for finding λ then I got λ as $-16/3$ and $16/3$ but function leads me to a complex value like $\mathbf{f(x,y,z)=-i 64/3}$ where is my fault? And sorry for my bad english.