I have noticed statements like the following on sectionals:
This would seem to suggest that a clearance is needed to "depart" any helipad, even if you are staying under the wedding cake. Is that true?
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The "Wedding Cake" literally defines the airspace, so for a the sectional part you listed above, the floor of the Class-B is at 3000 feet in the outer ring and 2000 feet in the inner ring, these heights are MSL.
Anything outside of the wedding cake is not Class B airspace. You may be confusing the Class B airspace with the Mode-C Veil that surrounds 30nm outside of most Class B airports, which only requires that you have an operating transponder, you are still allowed to fly around VFR squawking 1200 below the Class-B without any clearance.
The airspace under the wedding cake, provided you are not within a Class-E airport, is most likely Class-G. So no, you are not required to contact Tower until you want to enter Class-B airspace or if you need a departure clearance for IFR operations.