When a processor speed is given for a multi-core processor, is that the cumulative speed or the speed of the individual cores? For example, if we're considering an quad-core processor, and if the speed given in the "specifications" is 1.8 GHz, does that meant that the combined speed of the entire set of 4 cores is 1.8 GHz, or that each of these four cores has a speed of 1.8GHz individually?

In other words, if the printed spec is "quad-core 1.8 GHz", does that mean that there are 4 cores of speed 1.8 GHz?
Frequency is not cumulative. The chip runs at 1.8 GHz, each of the cores runs at 1.8 GHz, all four cores run at 1.8 GHz. If one car travels at 100 km/h and another car runs beside it at 100 km/h, you just have two cars running at 100 km/h, you don't have anything running at 200 km/h.

Instruction execution rate, on the other hand, is cumulative. If a single-core processor running f GHz can execute k instructions per second, then an n-core processor running at f GHz can execute n ⨉ k instructions per second*, just as our two cars together carry twice as many people as one car.

*In practice you won't see an n-fold increase in speed, as some resources are consumed in co-ordinating the cores.