The brain is as-per-now unbeaten if you measure (meaningful) operations per second (so not just moving bits) and the ability to learn fast and generalize local problems with common sense.
It is, however, especially bad at raw calculatory ability (as in adding, subtracting, multiply, divide, calculus). It also has a low memory capacity of estimated 120 GB, which leads to some interesting questions about our memory.
There are also multiple unknowns in neuroscience today. Are there neurons working together like transistors do in a flip flop memory cell? Is there storage going on the level below neuron connections, for example is part of the neuron's DNA or part of the neurons protein content used as storage device? We don't know.
Your superhuman, if it is constructed, could have a calculatory cell complex the size of a pinhead which helps him to calculate on a much higher, more precise level than any human normally does. As it is directly in his brain, they would use it instinctively. They would probably feel pain if someone claims improbable stuff, because they would have a natural feeling for probabilities... a thing where most of us are totally weak or even blind. As they factor this into their daily life, they will constantly be able to take better decisions and be also faster about it then the rest of us.
That today's scientific speculation about DNA level storage capacity could be made explicit for them. With that they would have loads more than those 120GB I mentioned above. Again, it is constructed, so proper indexing mechanisms would be there from the beginning. That means, they would not only have associative memory like us, but have a cell cluster that delivers information on explicit request, too. The ability to never forget birthdays, names, faces, interests, and private content about persons around them would give them a social edge which alone would make them lots more successful than any of us.
If you finally rearrange the consciousness so that it has two or three channels more than the standard, they could think in great detail about problems and find solutions before the others even get aware that there is a problem.
There you are. Two modules which fill gaps that our monkey brains have, either one not big enough to count toward your volumetric constraints, would give them a crazy advantage which the rest of us would perceive as "intelligence". If you add the consciousness channels, those two modules could even have a privileged access to it.
Now if you add some kind of antenna in their enlarged skulls, they could even send feelings and thoughts to each other with a band with high enough that their distinct personalities fade when they are near each other. Imagine two or more brains thinking together if they want. After that, they would be so far beyond humans, they would probably not communicate with us anymore. Or just the way we talk to a dog. Not good for a story. :-)