Last quarter, Oracle CTO Larry Ellison talked about the company's "rapid growth, scale-out phase" for its cloud businesses. Today, Oracle got a little more specific, predicting dramatic cloud growth in early 2016.

For its third quarter, which ends in February, Oracle expects revenues from software-as-a-service (SaaS) and platform-as-a-service (PaaS) offerings to grow 49 to 53 percent compared with the previous year. The growth gets more dramatic in the fourth quarter, when Oracle expects growth of 55 to 59 percent.

The numbers came out as part of Oracle's second-quarter earnings report today.

The cloud numbers come from a relatively small base. But they show how aggressively Oracle is pursuing that business.

In the bigger picture, Oracle is on the verge of a surge in profits, because the capital spending to build out these clouds is nearing completion. "I believe 2016 is a trough year for profitability as we move to the cloud," said Safra Katz, one of Oracle's two CEOs, during a conference call with analysts today.

Oracle predicts non-GAAP net income of 63 to 66 cents per share in the third quarter, compared with 63 cents in the second quarter.

The fourth quarter is when that "trough" would end, with net income climbing to 83 to 86 cents per share, the company predicts.

Oracle has infrastructure-as-a-service (IaaS) aspirations as well, but that business will grow less dramatically: 3 to 7 percent in the third quarter and 1 to 5 percent in the fourth, Katz said.

On today's call, Ellison reiterated that Oracle plans to be the lowest-cost competitor in IaaS. The company has revamped its architecture — kind of a "data center 2.0," he said — and has lowered its costs in the process.

Oracle has been boasting relentlessly about its cloud prowess, but its business is still dominated by more normal software sales. SaaS, PaaS, and IaaS combined for $652 million in revenues for the quarter ended Nov. 30, compared with Oracle's total revenues of $9 billion.

That total was down from the $9.6 billion that Oracle reported for its second quarter last year.

Oracle's non-GAAP net income beat expectations of 60 cents per share, according to Thomson Reuters. But the third-quarter profitability forecast was tepid next to expectations of 65 cents per share. In that sense, Oracle's second-quarter earnings were a lot like the first quarter's: a bland result spiced up by promises of the cloud.