Why not to build an altar from hewn stone?
In Joshua 8:31 I read about an altar of whole stones, over which no man hath lift up any iron. And in Exodus 20:25 I read also of an altar of stone, with the commandment "not to build it of hewn stone: for if thou lift up thy tool upon it, thou hast polluted it. My question is: why only whole stones?
In both cases you referred to it is theological reason. God by that commandments simply reinforced that salvation through the mediatorial and sacrificial death of Jesus Christ is ENTIRELY His work and His provision. Repeatedly the LORD instructed Moses to make the tabernacle precisely after the patterns He has shown him in the mount. Not a stitch or hook was left to Moses' imagination. This also was symbolized in the fact that the stones weren't cultured or hewn by men. The stipulation that it only were to be 'whole stones' could be reference to the fact that Jesus Christ was unblemished as a Lamb but also that none of His bones were broken.
As an extension of your question, isn't it beautiful how God provided this 'altar' in Ex. 20 (which functioned as the temporary tabernacle)! The people felt that they couldn't have communion with the Lord directly and feared that if He would speak again, they would die. The LORD's answered them by providing them an altar through which He would draw near to them and they could draw near to Him. This "altar" we just paused at when we commemorated the birth of Jesus Christ! Through Him we can have communion with the Lord.
May God bless us with that.