What process of photosynthesis can occur even when there is no light?

The Dark Reactions (a.k.a. The Calvin Cycle) can occur without the light. Sometimes they are also called the Light Independent Reactions for that very reason. Light is required during the light reactions because the energy from light (photon) is required to excite electrons. No such energy source is required for the Calvin Cycle because the energy has already been converted into a chemical form (ATP and NADPH) during the light reactions. The energy from ATP and NADPH is used to "drive" the Calvin Cycle (the accumulation of Carbon atoms from Carbon Dioxide). Carbon Dioxide and Rubulose Biphosphate (RuBp) are combined using the enzyme rubisco. The energy from ATP and NADPH is added (in several steps). The final molecule, gyceraldehye-3-phosphate (G3P) is produced. There is a fairly common misconception that glucose is the final product of the Calvin Cycle; but, it is actually G3P. Notice that none of these reactions (those of the Calvin Cycle) required light.

And don't forget, plants don't need light for cellular respiration either.