  Let $B_k$ denote the $k^{th}$ term of balancing sequence. In this paper we
find all positive integer solutions of the Diophantine equation $B_n+B_m = x^q$
in variables $(m, n,x,q)$ under the assumption $n\equiv m \pmod 2$.
Furthermore, we study the Diophantine equation \[B_n^{3}\pm B_m^{3} = x^q\]
with positive integer $q\geq 3$ and $\gcd(B_n, B_m) =1$.
