We present a robust algorithm for independent component analysis that uses the sum of marginal quadratic negentropies as a dependence measure. It can handle arbitrary source density functions by using kernel density estimation, but is robust for a small number of samples by avoiding empirical expectation and directly calculating the integration of quadratic densities. In addition, our algorithm is scalable because the gradient of our contrast function can be calculated in O(LN) using the fast Gauss transform, where L is the number of sources and N is the number of samples. In our experiments, we evaluated the performance of our algorithm for various source distributions and compared it with other, well-known algorithms. The results show that the proposed algorithm consistently outperforms the others. Moreover, it is extremely robust to outliers and is particularly more effective when the number of observed samples is small and the number of mixed sources is large.