First numbers that belong to both sets:
27000008,
27000064,
216000064,
216000512,
513000000,
729000216,
1027000000,
1728000512,
1729000000,
3907000000,
4104000000,
4123000000,
4914000000,
6013000000,
6517000000,
8029000000,
8216000000,
8587000000,
11557000000,
12697000344,
13832000000,
13851000000,
15542000000,
20683000000,
21411000000,
21488000625,
27729000000,
27894000043,
31256000000,
32832000000,
32984000000,
35359000768,
35879000976,
39312000000,
40033000000,
42877000376,
43946000000,
46683000000,
48104000000,
52136000000,
54873000000,
64125000000,
64232000000,
65728000000,
68696000000,
70497000000,
73017000000,
76951000063,
80236000000,
84266000000,
88239000024,
89995000914,
92456000000,
100711000000,
105489000000,
107919000000,
110656000000,
110808000000,
111321000000,
119377000000,
123506000000,
124336000000,
126217000000,
127062000000,
128375000000,
132678000000,
134379000000,
136591000000,
148941000000,
149389000000,
162351000000,
165464000000,
166383000000,
171288000000,
175959000000,
187551000000,
195841000000,
201159000000,
215010000504,
216027000000,
216125000000,
216783000000,
221832000000,
223152000344,
231849000000,
238329000000,
250048000000,
254079000000,
260691000696,
262656000000,
263872000000,
281827000000,
291319000875,
312039000000,
313111000384,
314496000000,
320264000000,
327763000000,
341271000350,
351568000000,
351981000000,
352261000000,
354227000328,
358036000000,
373464000000,
373977000000,
384832000000,
385415000000,
402597000000,
417088000000,
419634000000,
421876000000,
427350000168,
432944000125,
438984000000,
439003000000,
439101000000,
443889000000,
476749000000,
488375000000,
513000000000,
513856000000,
515375000000,
525824000000,
526204000448,
542851000111,
549568000000,
558441000000,
563976000000,
575883000000,
578097000000,
584136000000,
593047000000,
614250000000,
615608000504,
636785000000,
641888000000,
648613000000,
674128000000,
682803000000,
684019000000,
704599000840,
704977000000,
705912000192,
725965000768,
734854000680,
739648000000,
748683000000,
751625000000,
778813000000,
778904000000,
805610000384,
805688000000,
814625000000,
842751000000,
843912000000,
863352000000,
885248000000,
886464000000,
890568000000,
895978000125,
920673000000,
936152000000,
937062000000,
945035000000,
955016000000,
973243000000,
984067000000,
988048000000,
994688000000,
999960000832.