User blog comment:Kaido King of the Beasts/Chapter 862: Semi-Charmed Kind of Life/@comment-5741122-20170414041829/@comment-28966845-20170414133301

Nami's mirrage tempo was creating illusions, so they wuldnt be able to burst through the cake since they have no matter

2nd in order to create those illusions nami should be present inside the cake

So i think luffy somehow hid a mirror inside the cake and then they used brulee's powers to burst through while making em all mirror images of luffy. It would also explain why brulee was apologising to BM.