'by the way, the AI is definitely cheating, at least in begining of the game. Can the developers explain how the AI cheats?'
There is only one advantage the AI has over you at the start of the game.
They have been sending unmanned probes through the galaxy for longer than Man had been walking upright (possibly exaggerated, but basic premise remains. They know where the good planets are, it just took the invention of superphotonic flight, which humanity did just before the start of the game, to be able to colonize systems acceptably.
Otherwise they operate under the same conditions you do.
The apparent difference is because the AI currently focuses strongly upon combat related advancements, most of which have requirements that have a noticable improvement in certain fields, and upon improvements that increase production directly (apparently, again, with a preference toward military production).
The AI almost always runs at a slight deficit, which means that they have higher spending in one way or another.
As for your lower population, the AI almost allways colonises high-class planets in range first. If you're trying to compare 70 class 10s to three class 24s or 26s, it's usually going to take time for raw population to catch up. The low class pmlanets have lower morale (and thus lower production and population growth) and lower taxes (which indirectly lowers production by restricting your spending options).
And your comment about production cannot be accurate. The AI never colonises anything below class 15.