Cubes

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The following cubes should be memorized (at least through 203):

13 = 1

23 = 8

33 = 27

43 = 64

53 = 125

63 = 216

73 = 343

83 = 512

93 = 729

103 = 1000

113 = 1331

123 = 1728

133 = 2197

143 = 2744

153 = 3375

163 = 4096

173 = 4913

183 = 5832

193 = 6859

203 = 8000

213 = 9261

223 = 10648

233 = 12167

243 = 13824

253 = 15625

There are some numbers in which you should memorize even higher powers:

24 = 16

28 = 256

34 = 81

45 = 1024

25 = 32

29 = 512

35 = 243

54 = 625

26 = 64

210 = 1024

36 = 729

64 = 1296

27 = 128

211 = 2048

44 = 256

74 = 2401