Let Q(x) denote the number of positive integers \(n\leq x\) which are sums of three squares, and let \(\Delta\) (x) be defined by \(Q(x)=5x/6+\Delta (x)\). \textit{E. Landau} [Arch. Math. Phys. 13, 303-312 (1908)] proved that \(\Delta (x)\ll \log x\) as \(x\to \infty\). \textit{N. C. Chakrabarti} [Bull. Calcutta Math. Soc. 32, 1-6 (1940)] developed a formula for \(\Delta\) (x), based on the binary expansion of x, and used it to prove that \(1/6\leq \Delta (x)<(\log x)/(3 \log 2)+1/2\) where the bounds are sharp. Here the author shows that the function \(\Delta\) (x) has an average order and a normal order, both being 3 log x/(16 log 2). The proof requires a more elaborate formula for \(\Delta\) (x) which involves the positions of all the digits of the base 4 expansion of x.