The length swap is easy: 1 m = 100 cm. So how many cm³ in 1 m³? Tap the answer you believe:
1001
100
the length factor
1002
10 000
the area factor
1003
1 000 000
the volume factor
Pick one above — only one is the volume conversion.
Volume vs capacity, while we're here.Volume is how much 3-D space a thing takes up (cm³, m³). Capacity is how much liquid a container can hold (mL, L, kL). They're linked by 1 cm³ = 1 mL, so the same box has a volume in cm³ and a capacity in mL — just don't muddle the words.
When you cube the length, you cube the factor too: (×100)³ = ×1 000 000. The same trap hits cm²→m² (that one is ×10 000, i.e. 100²). Count the little ³ — it tells you how many times to multiply.