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Many applications deployed to public clouds are concerned about the confidentiality of their outsourced data, such as financial services and electronic patient records. A plausible solution to this problem is homomorphic encryption (HE), which supports certain algebraic operations directly over the ciphertexts. The downside of HE schemes is their significant, if not prohibitive, performance overhead for data-intensive workloads that are very common for outsourced databases, or database-as-a-serve in cloud computing. The objective of this work is to mitigate the performance overhead incurred by the HE module in outsourced databases. To that end, this paper proposes a radix-based parallel caching optimization for accelerating the performance of homomorphic encryption (HE) of outsourced databases in cloud computing. The key insight of the proposed optimization is caching selected radix-ciphertexts in parallel without violating existing security guarantees of the primitive/base HE scheme. We design the radix HE algorithm and apply it to both batch- and incremental-HE schemes; we demonstrate the security of those radix-based HE schemes by showing that the problem of breaking them can be reduced to the problem of breaking their base HE schemes that are known IND-CPA (i.e. Indistinguishability under Chosen-Plaintext Attack). We implement the radix-based schemes as middleware of a 10-node Cassandra cluster on CloudLab; experiments on six workloads show that the proposed caching can boost state-of-the-art HE schemes, such as Paillier and Symmetria, by up to five orders of magnitude.