Chulin 11a: To teach us that the Parah must be burnt whole, like it is Shechted whole. ¹

Sifri: To teach us that Melachah whilst burning the Parah renders it Pasul. ²

Zevachim, 113a: One places it on the arrangement of wood exactly opposite the etrance to the Ohel Mo?ed which, since it is compared to the Haza?ah of the blood (in the previous Pasuk) is cucial to the Mitzvah. Lkewise, burning it whole is crucial ¹ - since it is compared to the Shechitah (in Pasuk 3 ² ? Chulin, 11a).

Yoma, 42a: It means that Elazar should not be Masi'ach Da'as from the Parah while it is being burnt. ¹

Oznayim la'Torah: To emphasize that Elazar should watch the burning of the Parah, even though the smoke is bad for the eyes, and he may be tempted to close them.

Sifri: To teach us that if parts ¹ of it fall off the pile it is Pasul, but not a bone ² (By the same token, when the Kohen finishes sprinkling, ³ he must wipe his fingers on the cow - to ensure that the blood on his fingers is burnt as well - Zevachim, 93b).

Sifri: To include them should they fall off the Mizbe?ach, so that, if for example, same of the flesh falls off the MIzbe?ach and is not returned, it is Pasul ? but not a bone ? which Lechatchilah should be returned (since the Torah does not mention bones ? Torah Temimah).

Sifri: To teach us that, after sprinkling the blood, the Kohen must wipe his hand on the body of the cow ? so that the blood on his hand is burnt together with the it.

Rashi (in Pasuk 22, citing R. Moshe ha'Darshan): The Parah is burned just as the Eigel was burned (by Moshe).

Rashi: Another Kohen other than Elazar. ¹