Эта штука называется tiered cake stand, есть с общей осью (center column), есть без.

Center Column – As the name implies, a center column is used to stabilize the whole cake’s construction. Each tiered cake is placed on cake boards that have pre-cut holes in the center. A cake corer is then used in the lower tiered cakes, to push the center of the cake right down to the bottom. This is where the column is to be placed.

"We will stack the top tier of the cake [over the preceding cake layers] by sliding it over the central column"

Reference: http://www.reneeconnercake.com/how-to-stack-a-tiered-cake/

I've also seen "dowel" used as a verb, as in "dowel the top tier"

Верхний ярус торта мы будем садить на общую ось подставки.
->
We are going to slip the top tier over the central column.




Center Column Construction for Tall Tier Cake Stand at Bake Decorate Celebrate!
http://www.bakedecoratecelebrate.com/techniques/centercolumn...

== BEGIN QUOTE ==

Step 4: First Layer

Attach a 7 3/4 in. column to the prepared base plate with the bottom column bolt from underneath the plate. Slip the bottom tier over the column to rest on the plate. Set a plate that is one size smaller than plate below on top of the column.

== END QUOTE ==

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Note added at 6 hrs (2017-04-20 04:58:59 GMT)
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По идее, слой торта, в котором предварительно проделали отверстие, насаживают на неподвижную ось (закрепленную на подставке). При желании можно поступить наоборот — проталкивать ось снизу вверх через слой торта, но неудобно же... Впрочем, я не спец в этом деле.


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Note added at 13 hrs (2017-04-20 11:46:23 GMT)
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Нашел еще одну статью с фотографиями:

10 Baking Tips I Learned the Hard Way | The Huffington Post
http://www.huffingtonpost.com/sara-cann/ten-baking-tips-i-le...

== BEGIN QUOTE ==

10. Secure each layer. The architecture of a wedding cake is as following: Each cake is supported by a cake board round (basically a round piece of cardboard paper). Each cake layer is pierced with a dowel, or plastic straw, slightly taller than the cake itself, inserted about an inch in from the top layer. That way, the next layer will rest on these supports rather than the delicate buttercream. Lastly, each layer is threaded through a center dowel that ensures the cake won't fall over.

== END QUOTE ==

То есть вначале каждый слой протыкается штырем (is pierced with a dowel), а в заключение каждый слой надевается (is threaded through a center dowel).

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Note added at 13 hrs (2017-04-20 11:49:27 GMT)
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Извиняюсь, кое-что пропустил:

То есть вначале каждый слой протыкают штырем (is pierced with a dowel), а в заключение каждый слой надевают на центральный штырь (is threaded through a center dowel). Если я правильно понял, в данном случае в обоих случаях используется один и тот же штырь.