If I'm replacing a range with an oven and cooktop, do I have to change the breaker?
This isn't just an adding job

Your assumption that your oven &amp; cooktop combination requires a 70A breaker is actually incorrect -- this is due to the 220.55 demand factors in the NEC, as it's pretty implausible that the oven will be going at full broil and all four cooktop elements will be on full blast all day long on other than very rare occasions.  (That, and neither of your appliances require a dedicated branch circuit in their installation instructions.)

Applying the logic of table 220.55, note 4:


  
  Branch-Circuit Load. It shall be permissible to calculate the branch-circuit load for one range in accordance with Table 220.55. The branch-
  circuit load for one wall-mounted oven or one counter-mounted cooking unit shall be the nameplate rating of the appliance. The branch-circuit load
  for a counter-mounted cooking unit and not more than two wall-mounted ovens. all supplied from a single branch circuit and located in the same
  room, shall be calculated by adding the nameplate rating of the individual appliances and treating this total as equivalent to one range.
  


to our circuit gets us a total unfactored load of 14.625kW.  Since this is over 12kW, we must then apply 220.55 note 1 to the 8kW column C value for a single range to get the factored load:


  
  Over 12 kW through 27 kW ranges all of same rating. For ranges individually rated more than 12 kW but not more than 27 kW, the maximum
  demand in Column C shall be increased 5 percent for each additional kilowatt of rating or major fraction thereof by which the rating of individual ranges exceeds 12 kW.
  


Applying this logic gives us a 15% increase in demand, or 8*1.15 = 9.2kW, which is well within the capacity of a 60A branch circuit!  (In fact, you could run this combo off of a 50A branch circuit if you so chose.)  Given that the use of 220.55 factoring for range circuit sizing is expressly permitted by the NEC in 422.10(A), paragraph 4:


  Branch circuits and branch-circuit conductors for
  household ranges and cooking appliances shall be permitted to be in accordance with Table 220.55 and shall be sized in accordance with 210.19(A)(3).


we can safely say that you don't need to change your breakers here, as the factored load is considered the "maximum load served" for the purposes of 210.19(A)(3).