Smallest square that is a sum of powers

Choose an integer ratio $r>1$ and add up the geometric progression $1+r+r^2+\cdots+r^{k}$ with at least three terms. What is the smallest perfect square that can arise this way? (For instance $1+2+4+8+16+32=63$ just misses a square.)

121. Three terms never work, since $r^2<1+r+r^2<(r+1)^2$. Searching small ratios and lengths, the first hit is $1+3+9+27+81=121=11^2$; the next is $1+7+49+343=400$.