Disagreement by Stan

Stan gave us a nice puzzle with a little bit of maths. The extra letters in wordplay gave us the message SMALLEST NUMBER SUM OF TWO CUBES IN TWO WAYS. In four cells of the grid two letters had to be fitted. These letters were CU & BE, twice, in the first cells of across words. The numbers in these cells were 1, 9, 10 and 12. The cubes of 1 & 12 add up to 1729, as do the sums of 10 & 9. 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan. In Hardy's words: “I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
The clashes in cells had to be resolved to display the name RAMANUJAN diagonally (the discarded letters spelled GH HARDY!) and the subject of the disagreement was the number 1729.

Extra letters in wordplay are shown in []

Across
1 Tail of rabbit and head of rat caught in pasture - what you might get in a canteen (6)
CUTLERY [S]CUT + R(at) in LEY
6 Introductory section is a source of enlightenment (4)
ALAP A LA[M]P
9 Get away to live by turbulent Onega (5)
BEGONE BE (live) + Anagram ONEG[A]
10 White cell lab regenerated around nucleus of corpuscle (6, two words)
CUE BALL Anagram CE[L]L LAB + U (central letter in corpUscle)
11 Inlaid work boss returned in lines (4)
BUHL HUB reversed in [L]L (lines)
12 Worker, having enough power to capture gunners, can be carried (7)
BEARABLE RA in BE[E] ABLE
14 Pressed Australian boarding Concorde? (3)
SAT A (Australian) in [S]ST (supersonic transport)
16 Missing strategical move, on the attack and ready to mate (6, two words)
ON HEAT ON [T]HE AT(tack) less TACK (strategical move)
18 Good-for-nothing belonging to start of defence runs around wing back (5)
IDLER EL (wing) reversed in I[N] D(efence) R (runs)
20 Lee's aunt flying kites (7)
ELANETS Anagram LEE’S A[U]NT
22 French ship originally carried bread (5)
FRANC FR (Fench) + [M]AN + C(arried)
24 Bedroom assistant is a fast mover (6)
RUSHER [B]R + USHER
27 Measure of her age starts to reduce embarrassment (3)
ARE A[E] (aetatis, of her age) + RE (initial letters)
29 Advisory council wreck plan to trap Ireland's premier on the inside (7)
CABINET C[R]AB (to wreck)+ NET
30 Goddess starts to get silly after imbibing ambrosia (4)
GAIA G[S]AIA initial letters in clue
31 This duct clamp could end up in permaculture (6)
URETER Compound Anagram PERMAC[U]LTURE less CLAMP
32 Master bringing in boat calls for attention (5)
AHOYS [M]AS including HOY  

33 Rubber cushion - number one in relief inside for the old (4)
TYRE R(elief) in T[O] YE
34 Few dare to turn over bank (6)
DRAWEE Anagram [F]EW DARE
 
Down
1 Dried fruit Elizabeth found in young animals (4)
CUBEBS BE[T] in CUBS
2 Deliberately avoiding country-and-western broadcast, crazy once end's removed (8)
TRUANTRY Compound Anagram COUNTRY AND [W]ESTERN less ONCE END’S
3 John het up about American hate (6)
LOATHE A (American) in LO[O] + Anagram HET
4 Be clear about dropping absent insurgent (4)
REBEL Anagram BE [C]LEAR less A (ansent)
5 University after first of researchers in pay out scale (7)
VERNIER R(esearchers) + [U]NI in VEER
6 Down cake soaked in rum and a drop of Shiraz (4, two words)
À BAS [B]ABA + S(hiraz)
7 Trademark twister comes after ball spun lacking length (5)
LABEL Anagram BALL less L (length) + [E]EL
8 Endless delight with a low piece on the side? (6)
PLEURA PLEA[S]UR(e) with A moved down
13 Goddess that is after a first in theology shrouds heavenly body (7)
ASTARTE STAR in A + T(heology) + [I]E (that is)
15 Cape peninsula starts to lead excursions outside (8)
PELERINE PE[N] (peninsula) + L(ead) E(xcursions) + RINE (rind = outside)
17 Overuse bank to clear last of pay (7)
HACKNEY HACK (bank) + NE[T] (clear) + (pa)Y
19 Anything about very loud scoundrel lacking resistance is surplus (6)
OFFCUT FF (very loud) + CUR less R (resistance) in O[W]T (anything)
21 Stag has carved up trees (6)
SHADOW Anagram HAS + W[O]OD reversed
23 Warning light - beware moving when end of lane becomes motorway (5)
AMBER Anagram BE[W]ARE changing E (linE) to M (motorway)
25 Katie's wobbly belly (4)
KITE Anagram K[A]TIE
26 West Yarmouth accommodates seaside rush ... (4)
STAR Hidden weST [Y]ARmouth
28 ... the tide's here at last - get rest from work! (4)
EASE [S]EA’S + E (last letter in HERE)