Sum of $\sum_{n=0}^{\infty }\frac{1}{4^{(n/3)+1}}$ Find the sum of $$\sum_{n=0}^{\infty }\frac{1}{4^{(n/3)+1}}$$

prove by induction that for the definite sum holds
$\sum_{n=0}^{m}\frac{1}{4^{\frac{n}{3}+1}}=-1/12\, \left( {2}^{2/3}+2\,\sqrt [3]{2}+4 \right)  \left(  \left( 1/2
\,\sqrt [3]{2} \right) ^{m+1}-1 \right) 
$
