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The addition of three two digit numbers gives a three digit number  which can be a cube where the single digit numbers 1 to 9 exit once only . one such example is 

83 + 54 + 79 = 216 = 6³   Can you work out for few more examples 

The cube numbers can end with any digit ,however its number digit will be 1. 8,9 only. By simply interchanging the ending digit of the two digit numbers more examples can be obtained.

84 +59 + 73 = 89 +53 + 74 = 216,

A variant of this problem is  the addition of two three digit numbers with a resultant of  a three digit number

146  + 592 = 738

154  + 782 = 936

159 +327 = 486

182 +763 = 945

183 + 492  = 675

193 +275  = 468

218 + 349  = 567

317 + 529 = 846 

By interchanging the equivalent digits in the numbers  added together , one can get more solutions but  there are very few solutions with resultant being a square. One example is here  

143 + 586 = 729 = 27² Find your own solutions.

194  + 382 = 576 = 24²

369  + 415 = 784 = 28²

 Dr.M.Meyyappan, Thavakkai Academy of Creative Thinking and Skill Development