Answer
$\exists x[(x>0) \land \forall a \forall b \forall c(x\ne a^{2}+b^{2}+c^{2})]$
Work Step by Step
Let the domain be all integers.
An integer is positive, if the integer is larger than 0.
We can rewrite the given sentence as: "There exists an integer x, that is positive and for all three integers a, b and c, x is not the sum of the squares of the three integers."
$\exists x[(x>0) \land \forall a \forall b \forall c(x\ne a^{2}+b^{2}+c^{2})]$
