RGB Gradients Generation

JavaScript (ES6), 130 bytes

g=
(f,t,n)=>[...Array(++n+1)].map((_,i)=>f.replace(/../g,(e,j)=>((`0x${e}`*(n-i)+`0x${t[j]+t[j+1]}`*i)/n|256).toString(16).slice(1)))
;
p=_=>g(f.value,t.value,+n.value).map(e=>o.insertRow().insertCell().appendChild(document.createTextNode(e)).parentNode.bgColor=e);

<input id=f value=e14f09><input id=t value=9a04f6><input id=n value=4 type=number><input type=button onclick=p() value=Go!><table id=o bgcolor=black cellpadding=4>

Dyalog APL, 44 bytes

Prompts for N, then Beginning-color, then Ending-color. Needs ⎕IO←0 which is default on many systems.

h[↑⌊B∘+¨(⍳2+N)×(-/E B←(h←⎕D,⎕A)∘⍳¨⍞⍞)÷1+N←⎕]

h[...] index into h (which has a value when we finish evaluating the the bracket's content)

 N←⎕ prompt for numeric N (4)

 1+ add one to N (5)

 (...)÷ use that to divide the result of...

  ⍞⍞ prompt for two character strings ["7E0E7E","FF3762"]

  (...)∘⍳¨ find the indices of the each string's characters in...

   ⎕D,⎕A Digits followed by Alphabet

   h← assigned to h

  now we have "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"

  E B← assign the indices to E and B [[7,14,0,14,7,14],[15,15,3,7,6,2]]

  -/ subtract and enclose B from E [[-8,-1,-3,7,1,12]]

  the result so far is [[-1.6,-0.2,-0.6,1.4,0.2,2.4]]

 (...)× multiply this by...

  2+N two plus N (6)

  ⍳ first integers [0,1,2,3,4,5]

 this gives us [[0,0,0,0,0,0],[-1.6,-0.2,-0.6,1.4,0.2,2.4],[-3.2,-0.4,-1.2,2.8,0.4,4.8],...]

 B∘+¨ add B to each [[15,15,3,7,6,2],[13.4,14.8,2.4,8.4,6.2,4.4],[11.8,14.6,1.8,9.8,6.4,6.8],...]

 ⌊ round down [[15,15,3,7,6,2],[13,14,2,8,6,4],[11,14,1,9,6,6],...]

 ↑ make list of lists into table

[[15,15, 3, 7, 6, 2]
 [13,14, 2, 8, 6, 4]
 [11,14, 1, 9, 6, 6]
 [10,14, 1,11, 6, 9]
 [ 8,14, 0,12, 6,11]
 [ 7,14, 0,14, 7,14]]

here we index into h, giving

[["F","F","3","7","6","2]
 ["D","E","2","8","6","4]
 ["B","E","1","9","6","6]
 ["A","E","1","B","6","9]
 ["8","E","0","C","6","B]
 ["7","E","0","E","7","E]]

which is the same as

[["FF3762"]
 ["DE2864"]
 ["BE1966"]
 ["AE1B69"]
 ["8E0C6B"]
 ["7E0E7E"]]

and prints as

FF3762
DE2864
BE1966
AE1B69
8E0C6B
7E0E7E

TryAPL online!

Pyth - 35 bytes

Horribly golfed, just gave up.

j++hQsMCm.HMsM:F+dc-FdvzCmiR16cd2Qe

Try it online here.

Example: