More common way to say "squared", 二次方X or X的平方？
I think you don't bother to find what's correct, both 米每二次方秒 and 米每平方秒 are understandable.

Basically, there are some statute describe the general rule for unit pronounciation . But I can't find the data source, so I don't post the rule here. 

My rule is, just like in english, read all x³ to 立方x, all xᒾ to 平方x expect /sᒾ . 

For example read 

kg/m³
kg        /     m³
千克      每    立方米
kilograms per cubic-meter 


In most cases $ x \in {m,cm,mm,s}$, if oneday I have to read the gravitational constant G(6.67E-11 N*mᒾ/kgᒾ), I most probably read 每平方千克.

Below are reasons why "米每二次方秒" more common than "米每平方秒"(from the perspective of Bayesian inference.) I think it's just a convention. It's a huge project to find exactly why.
For the pronunciations of other common units, you can also find them in my links.



Statute law

It shows there are only one correct pronunciation.


中华人民共和国国务院公报 page 572 中华人民共和国计量单位名称与符号方案  from 中国政府
中华人民共和国计量单位名称与符号方案（试行） from 北京法院法规检索
《中华人民共和国法定计量单位使用方法》 , it is hosted on serveral unofficial web, I cannot find an official site.


Publication

This solved your question of "中国数学家" .


大学物理(高等院校物理系列教材)
常用非法定计量单位与法定计量单位的对照及换算表 from 中国大百科全书数据库
&amp; 附录二 非法定计量单位与法定计量单位换算表 from CNKI jiangxi


Web data

This solve "the most common" problem.

Use double quotation marks and search by yourself to see what use them!
One publication only has one form


google books ( 194 compared to 9 )
google scholar ( 14 compared to 2 )
google result (15700 compared to 4960)


Don't use baidu, the result include "米每二次方秒" and "米每平方秒" even if you use double quotation marks.

Argument against

baike

米每平方秒
加速度(米每二次方秒)

see the link above, it's self-contradictory. 
Due to web incompatibility, I can't amend it. 
Also, the *former* baike article don't have source material.


google translate 

`Metre per second squared` -&gt; `米每秒平方`
`米每二次方秒`-&gt;`Meter every second second`
`米每平方秒`-&gt;`Meter per square second`


Baidu translate 

`Metre per second squared`-&gt;`米/秒平方`
`米每二次方秒` -&gt; `Metre every second square second`
`米每平方秒` -&gt; `Metres per square second`


Others

FWIW, believe Wikipedia, when can't find in Wiki then use baike.